During the events of Thor: Ragnarok we see
Surtur destroy Asgard and Thor and the team leave
but we don't get a clear conclusion as to
Surtur and Hela's demise.
Did Surtur die?
With his Eternal Flame restored, Surtur was considered as powerful as Odin and with enough craft or raw power, he could have found a way to survive.
Paradoxically, The Asgardians and the realms they had lay claim to would be considered technologically advanced. So advanced, in fact, their science resembled magic. This means the destruction of Asgard may have been prophesied or predicted but the specifics were not spot on.
The citizens of Muspelheim and the other members of the Nine Realms were as tough and nearly immortal as the Asgardians. Thus properly empowered with the Eternal Flame, Surtur could effectively be unable to be killed which may have explained why the Eternal Flame, the source of Surtur's power, was stolen by Odin all those years ago.
Surtur was destined to be involved in Ragnarök in which Asgard would be destroyed and reborn in an endless cycle. He would cross the Bifrost and destroy Asgard with the Twilight Sword. (Thor #200)
Since the Marvel Cinematic Universe has taken many liberties with the legends of the Norse and their end days during Ragnarök, it is possible we have witnessed one of several things:
A false Ragnarök: In the comics, there were events which may have brought temporary destruction to the people or the property of Asgard sufficient to have been thought to be Ragnarok by the inhabitants. These false Ragnarök-events take place because Odin is attempting to avoid the prophecy by altering events he has learned of when he sacrificed his eye and hung from the World-tree in search of Wisdom.
In a false Ragnarök, Odin manipulates people, events, and things in order to prevent the loss of all the gods by sacrificing one or more persons in some insane scheme. Strangely enough, many of these false-positives delay but have not averted the final arrival of Ragnarök. In some cases, the Asgardians are cast down into mortal guises and have to be regathered, hidden from forces which might have destroyed Asgard, they are able to return if certain magical conditions are met.
It would appear in the MCU, we are seeing an event which resulted in the destruction of the place called Asgard, but many of its people survive.
Since we are not certain what we are seeing, it might not be the wisest course of action to assume everyone died, just because we see Asgard, the city proper, the realm proper, disappear from sight.
Did Asgard go somewhere? Was its portal closed? Was it a pocket dimension? Did said dimension collapse? We are not sure of any of these things because much of the nature of Asgard was outside of our purview and we weren't told HOW Asgard worked, only that it did.
As a result, we are lead to believe that Surtur who knew he was part of a prophecy to destroy Asgard, believed he had finally been granted an opportunity to do so. But did he? Does he destroy the dimension or merely a temporary holding facility where the Asgardians kept their stuff?
I suspect this was a false Ragnarök because so many of the conditions for the Twilight of the Gods had not been met. Yes, Odin died, but the prophecy said he would die in the slavering jaws of the Fenris Wolf after it had eaten the sun...
Thor was expected to die battling the horror of Jormangandur, the Midgard Serpent, killing the monster by dying from its venom, nine steps later. The other Asgardians were supposed to come to equally gruesome ends.
Mythologically speaking, at the end of Ragnarök, all the gods are purportedly slain and only a few mortals were to remain to bring about a new world. That didn't happen.
The Fenris Wolf is lost, the Midgard Serpent didn't appear, Hela did appear and try to take over Asgard, something unexpected by all accounts except by Odin.
All of these things sound terrible but did not ultimately equal the End of Asgard and all its gods. Sounds like to me, the Norse Gods have weathered another false Ragnarök and its up to King Thor to lead them forward, with the crisis temporarily averted.
Like most things comics-related: "Is Surtur (or Hela) dead?" is a question which does not have an assured answer. It will depend on whether a writer of a future story can contrive of a reason for Surtur or Hela to survive and then craft a story we are willing to accept.
Given Hela's popularity, she indeed may return to plague or save the Asgardians another day.