In Spider-Man: No Way Home, Peter does not want to send the villains back to their universes to die. He wants to "fix" them (cure them). It was implied that would keep them from dying, but how? Was this explained?
Yes, it was explained in this dialogue between Peter Parker and the villains while Doctor Strange has them all incarcerated:
Otto Octavius: You could've just left us to die. Why didn't you?
MJ: Because that's not who he is.
Peter Parker: I think I can help you guys. If I can fix what happened to you, then when you go back, things will be different and you might not die fighting Spider-Man.
Peter Parker: I can't promise you guys anything, but at least this way, you actually get to go home and have a chance. A second chance. I mean, come on. Isn't that worth trying?
Curt Connors: Trust me, Peter... When you try to fix people, there are always consequences.
Peter Parker: I mean, you don't have to come. I also didn't know that you could talk. [The Lizard growls in disapproval] But if you stay here... you're gonna have to deal with the wizard.
Curt Connors: So, we go along, or die. Not much of a choice, is it?
Flint Marko: I just wanna go home.
Max Dillon: Well, I myself don't wanna be killed, especially by a guy dressed like Dungeons & Dragons, so... what's your plan?
Peter Parker: I have it all under control.
'Fixing' the villains will give them a second chance at life, helping them avoid the choices that will ultimately lead to each dying fighting 'their' Spiderman.
It was the villains' "defects" that caused them to die: e.g. Green Goblin's alter ego was Norman's last consciousness. Doc Ock's arms were in control, causing him the urge to rebuild the reactor which ultimately made him drown. Electro also was killed, as he went power-heavy and tried to contain the city's power.
These "defects" are what caused the villains' death, and removing them would save them.