If the ringbearer died

[Tigerlily Gamgee]

Well, we see Sam take it in the books when he thinks Frodo is dead. Sam would be the only other person in Middle Earth that could even attempt the burden.
Who knows if he would succeed or if he would eventually break down from grief...
Galadriel can't take it because she would've been easily corrupted by it because she already possessed Nenya - the same goes for Gandalf and Elrond and their rings.
Though Aragorn is a strong man, he is still a man - and they are the weakest of soul... so, though he may be strong at first he may eventually succumb to the power.
So, yes, I think that if Frodo died then Middle Earth probably would've perished. As Galadriel says, "If you cannot find a way, no one will."