Are there any canon sources which indicate that the Dominion was aware of the Borg? If so, do those sources indicate what the Dominion planned to do about them?
I find it hard to believe that they didn't know about the Borg, yet I don't recall seeing anything in any of the TV series or movies about what the Dominion might do about the Borg.
On a side note, it seems to me that the non-Borg races of all quadrants would have been done well to band together to take down the Borg.
In DS9 itself, the Borg were never involved in the plot. (After the first five minutes, which were a flashback to off-screen events during The Best of Both Worlds, Part 2. Here’s a decent list of Borg mentions in DS9.)
As such, the Dominion’s relationship to them was never explored. They do occupy very distant regions of space, so until the Founders reached the Alpha Quadrant via the wormhole, it’s conceivable that they just never encountered them (although, as Nate Watson notes in his answer — which is good, go vote it up! — apparently the Borg did have some sort of facility in the Gamma Quadrant).
Once the Founders did reach the Alpha Quadrant, they seemed to be fully occupied with manipulating and fighting the majors powers there, rather than worrying about a distant enemy of those powers who had only made two significant incursions into the region, on both occasions with a single ship that was destroyed.
(Out-of-universe, DS9 left the Borg to TNG and Voyager; presumably the writers felt it would do better if it had its own identity as a show, with its own villains. Ronald D. Moore confirmed, but did not explain, that decision in a web chat.)
There is another question that asks about assimilated Founders, and the answer describes a DS9 novel where a Founder discusses a failed Borg attempt to assimilate it.
That suggests that the Borg might not have been much of a threat to the Founders themselves. In DS9, the Founders wanted to impose order across then galaxy, seemingly to pre-emptively defend against mistreatment from “solids”. It’s possible that they wouldn’t mind much if the Borg assimilated everyone else; it’s less work for them to do.
(Although, as mg30rg comments, that doesn’t mean the Borg couldn’t or wouldn’t have killed Founders if they’d encountered them; just that they might not have been able to assimilate them.)
Though there's little canon evidence, the answer is probably yes.
For starters, it's a pretty safe bet that the Borg are aware of the Dominion. We saw in "Endgame" on a map shown by Seven (who probably knows what she's talking about) that the Borg have some kind of facility in the Gamma quadrant. On top of that, the Dominion's cloning technology would be extremely useful to the Borg, so naturally there was probably some investigation on the part of the Borg.
On top of that, the Borg have a species number for the Ferengi, which are an Alpha/Beta quadrant power; which means that the Ferengi are farther away from the Borg than the Dominion is far from the Borg, since the Dominion is in a neighboring quadrant to the Borg. So the Borg probably have at least heard of the Dominion, simply because the Dominion is geographically closer to them than a species they have encountered. Based on this, the Borg have probably encountered the Dominion at least once.
Frequently, during Borg encounters, there's often a survivor or two, such as Guinan, or the people Seven saved in "Dark Frontier", so given that the Borg have probably encountered the Dominion at least once, there was probably at least one survivor, who probably told the Dominion government "Hey, I'll take what I can get in terms of Borg defense, and the Dominion is worth a shot".
So in summary, based on what we know in-universe, it's probable that the Dominion has at least one person who has had some kind of Borg encounter. So from canon sources, the answer is "Probably yes."
Edit: Additionally, the Dominion had spies in Starfleet for a while, after first contact, but before the war started formally. Given that the existence of the Borg is public knowledge in the Federation, and given that this is a massive military threat, the Dominion spies almost certainly told their government about the Borg.
On a side note, the Dominion claims to be over 10000 years old "as of the 24th century", whereas we know the Borg were a minor power 900 years ago, having only assimilated a handful of systems and being easy to resist. "Dragon's Teeth". If we extrapolate from that, the Borg are probably about 1500 years old at most. Prior to founding the Dominion, the Changelings were a migratory exploring species. If the Dominion is aware of the Borg, it's definitely from knowledge obtained from member populations, rather than information the Changelings discovered in their peaceful era.
Not quite a "canon" source, but the first mission of the Borg campaign in Star Trek Armada 1 has you assimilating a Dominion cloning facility.
There is nothing in the canon to be certain...even having a Borg facility in the Gamma Quadrant does not by itself provide certainty, since the Gamma Quadrant is large and nothing says the Dominion occupies or has even explored all of it. Their spies in the Federation, like all spies, would be looking for specific things...the Borg, among a very long list of species which the Federation had previously encountered, may very well escape conscious notice, just part of the huge mass of background information all intelligence activities pick up.
It is more likely that the Borg know of the Dominion: they are more active explorers, they never forget or overlook anything, and with Transwarp technology distance is not the issue for them that it is for everyone else, including the Dominion. And since the entire collective knows everything every assimilated member ever knew, it would only take them assimilating one person who knew about the Dominion for the collective to know of it. And if they assimilated a JemHadar or a Vorta, they know about the changelings specifically and in detail.
It is all speculation, of course...but looking back at DS9 and Voyager specifically, I've always felt it was only a matter of time before the Dominion would hear that "Resistance is Futile."
As I see it Borg is aware of most of Milky Way races and cultures, as they poses very advance Transwarp tech (not to mention 4 Transwarp Hubs) witch allows them to send they scout ships all around the galaxy in short time; but knowing that some culture like Dominion or any other exist does not means that the Borg will automatic go to assimilate it. Borg is interested in advance and sophisticated technology and so they would advance on specific targets that they see as something that will advance them closer to 'PERFECTION', or significantly advance their technology or biology, as we sign in their choice of conflicts like species 8472 from fluidic space (they are 'apex of biological beings'), and other extra-dimensional spaces, or realms that contains other extremely advanced lifeforms and spaces from which they would add to their own (7of9 was talking to Harry Kim of one of them, and I believe that at least one more was mention somewhere in Voyager series)... So for them galaxy as we perceive it is just a surface, and just one of many dimensions witch they can access with their tech, and they are allways looking for more and better tech...
Dominion is not so much a advance culture as one advance and highly evolved species (Founders), which control massive army of cloned, drug addicted soldiers whom don't live more then 10 years, and also cloned genetically engineered administrators Vorta; with their army Founders subjugate smaller cultures and individual races and planet from witch they take what they need for their warmachine, AND also enforcing ORDER, at least their vision of it (witch they as changelinks need; and also that which they control can' hurt them).
From this Dominion and Borg may be aware of one another, but direct conflict would not be in interest of neither one of them. Dominion can NOT hope to defeat the Borg no matter how many soldiers they clone, and Founders could NOT possibly hope to control Borg or to bring 'order to chaos' here, I mean Borg drones cannot function without their mechanical and computer parts, so only way would be to destroy the WHOLE collective (hardly with just army of Jem'Hadar, and lots of ships), or rehabilitate drones one by one as 7of9 was by Voyager EMH and Capt. Janway (also not very likely, they are not very humanitarian by nature, and also they see solids more like pets at most, or like unimportant so why bother)... So they would probably keep out of site, keep Borg unaware of them (i mean Founders; as I sad Borg would probably like to know more about so evolved species); even if thair warship meet with Borg in space, write of the loss and go on (Jem'Hadar and Vorta are expendable). The Borg on the other hand, well if they see something they want to take in some Dominion world they would assimilate it, no problem; raw materials that they need to build what they need they can find closer to home; to them Dominion is too one dimensional, too unimportant to go for directly, but in time as they grow, if nothing stops them, they will assimilate Dominion controlled worlds one by one; but Founders will be a bit harder to find :)
There is no sure fire way to know whether the Borg and Dominion actually interacted. If they hadn't, it is possible both at least know about each other. The Borg usually tend to go for technologically more advanced cultures... and the Dominion didn't seem that much more advanced than the Federation. All in all, both seemed on pretty much equal technological standings, with both excelling or falling behind one another in a few areas - overall, they seem more or less similar.
This is one of the reasons the Borg wouldn't necessarily fiddle too much with the Dominion. The Dominion took 2000 years to get where they are... the Federation did the same 10x faster... mainly due to the concept of sharing resources, technology, ideas, automation (and no money).
I would imagine that the Federation might prompt a bit more interest than the Dominion in the long run as far as the Borg are concerned, since the Federation demonstrated an ability to adapt relatively quickly and think outside the box. That's why they might expend some resources by sending occasional ships towards the AQ...
They might have done the same towards the Dominion as well. I would imagine that larger organizations such as the Federation, Dominion, Klingons and Romulans would warrant a bit more caution in terms of full blown assimilation because they are relatively big interstellar collection of societies.
Hence the Borg might prefer sending an occasional ship to test their breakthroughs and keep an overall eye on them.
We can be very confident that the dominion is aware of the Borg. Other answers here point out that the dominion infiltrated starfleet with changeling spies. The Borg represent the greatest existential threat that the federation is aware of. The federation takes that threat so seriously that, at the time of DS9, they had begun designing starships with the sole intent of combating the Borg. The Defiant class vessel (https://memory-alpha.fandom.com/wiki/Defiant_class) is an example of this. The Dominion would surely have been interested in learning everything they can about the Defiant class. It was among the most combat capable ships starfleet could field.
Given that the Borg threat is not classified, and the very significant effect it has on the culture of starfleet, I have difficulty imagining that the Dominion did not learn of the Borg while conducting routine espionage.
i don't think that is directly mentioned any where; but in the Dominion at least Founders must be aware of the Borg; they must have lost ship or two in space, or planet, or a colony to the Borg. If not that at least one Changelink must have encountered if not Borg directly then at least some evidence of them, or refugees who are running from the Borg; in any way empire size of the Dominion must have made some sort of contact with the Collective !
Just the isolationist way in which the Founders live, and planets they choose for homeworld; no tech, no structures, nothing but an arboretum could be seen as a way not to invite attention from anyone. As we know Borg are interested in sophisticated tech and raw resources, so they would totally ignore it.
So just from that we can assume that they know that are a threats to them in the surrounding parts of the galaxy, and things which are worse then solids or some species with which they are currently in war...
Scorpion and Dark Frontier and Endgame gave us some idea of the scope of the Collective, but we've never really seen the full scope of the Dominion- only a small fraction of their forces went into the Alpha Quadrant, right? I feel that the borg would want a)cloning technology and b) jemhadar to be drones, but most of all is the really really advanced dominion tech- polaron phasers (the Jemhadar et al) and cloak piercing scanners (once more unto the breach)? Long range transporters (Covenant)? tractor beam immunity (The Jemhadar)?. With all these advantages I think that the dominion could win a large, quick decisive war if for example they invaded borg space in staggered waves to arrive at the same moment and used polaron weapons to inflict crushing damage before the borg adapted. You could say the same about pretty much any other species but the dominion probably has the most resources and inclination to attempt something like this. (Oh- esp if the main dominion got their hands on a Breen weapon). On the other hand, if the borg identify the mDominion first and begin their usual gradual scout and assimilate campaign, getting time to adapt, it looks pretty grim for the founders.
But what about the military worth of the Founders themselves? Could they gum up the works of the Borg- possibly literally? idk about that. I still give the Dominion long odds unless they can launch an overwhelming first strike, and since they don't have transwarp, not good odds.
It is quite possible that some species like the Organians has labored over the millenia to prevent agressive powers from coming into conflict with each other. After all, they prevented a war between the Federation and the Klingon Empire; how much more would they want to keep the Borg and the Dominion seperate?
