What should happen? The thing that should have happened in ME2.
- Oh, no! Shepard's dead! Quickly, let's bring him/her back to life.
- Wait. Won't that take a lot of time and cost us ridiculous amounts of money?
- Well, er, yes.
- So why don't we use those resources to build weapons and warships, and gather armies against the Reapers instead?
- Brilliant! Why didn't I think of that?
More realistically, if Shepard dies, s/he doesn't do whatever s/he does in Arrival, so the Reapers come early and kill everyone.