Obviously, when humans die in Supernatural, they go to heaven or hell, or just stick around as ghosts. But what happens to Angels and Demons? We all know (in the show) that they exist, and that you can kill them with special weapons, knives, and get rid of them with weapons.
But what HAPPENS to them?
Do they just dissipate into nothing?
Do they go to purgatory as well as monsters?
Do they go back to heaven/hell?
What?
Angels
It is stated in the flashback scene of "The Man Who Would Be King" that angels do not have souls, they simply exist. When angels die, they don't go to Heaven, as can be concluded from the whole Civil War arc, because then there would just be an unlimited supply of angels. Additionally, even Purgatory is limited to creatures with a soul, which can be concluded by "The Man Who Would Be King" meaning angels don't end up there either, they would have to just "wink out" like the light on a candle being snuffed.
Demons
The same issue applies with demons, essentially. If when they were killed, they ended up back in Hell, there would simply be an unlimited supply of demons. Since they are technically just an altered human soul, though, that means there IS still a soul there. That basically just makes them supercharged ghosts, as is explained in "Weekend at Bobby's". They can additionally be killed the same way as a human spirit, by burning the bones (also "Weekend at Bobby's").
What happens to demons when they die would have to be the same thing that happens to a vengeful spirit. My personal guess is that their soul goes back to how it was before they became demons. Crowley would become Fergus McCloud again, for example.
What leads me to that conclusion is that, as shown in "Taxi Driver", when Sam went to Hell to rescue Bobby, who was previously a vengeful spirit. One could infer that they are just sent to either Heaven or Hell, but it would not make sense for them to go to any of those places as a demon; they would need to be a human soul. The other option would be that they would be sent to Purgatory. That, however, would not be explained because demons are human souls and Purgatory is "not a place for human souls," as explained in Dean's various flashbacks to Purgatory in Season 8.
In the fourth episode of season thirteen, it's revealed that they go to the Empty:
Nothing but Empty. [...] Angels and demons, you all come here when you die [...] sleeping an endless peaceful sleep. (Cosmic Entity)
I'd think angels, being soulless, simply cease to exist and I imagine demons have their souls purified (having gone through penance enough having been tortured to the point of becoming demons) and sent to heaven.
It seems like they cease to exist, based on canon, though some AU's like Lightborn (http://kenu.deviantart.com/gallery/37647591?offset=0) propose that they end up in Purgatory too.
Maybe, the Angels are reincarnated as humans or sent to an adjacent of Purgatory/ Limbo Realm in which time and past does not exist.
Angels: Born as humans as seen an angels grace being cut out becomes human and when they "die" the grace explodes killing the host.
Demons: probably sent to heaven because they have already been tortured and whent throw the proses of hell completely and human souls can't cross to purgatory except after killing a leviathan and being cought in the goos explosion.
(Monsters in Purgatory): maybe become human again because they were human souls.
