It'd be poor form for a GM to have a player still get more or less a "game over" despite burning Edge. If the team does nothing to recover them after they go down (a dumb move, considering interrogation and torture to find accomplices is a thing) then they would get captured, but rather than "life in prison, make a new character" there should be a continuation, maybe an attempt to get the guy out.
Honestly, if a character gets captured, it's still a 'write up a new character' situation. On getting captured, all their gear is now gone, and since they just had to burn Edge to survive WITH all their gear, they're just going to end up in a downward spiral from there. Not to mention that with how much things cost, it's unlikely they'll ever be able to recoup the loss even outside that.
Most characters likely don't have that much gear they carry with them all the time, but it'd be a strong loss. I'm not saying I'd force the player; if they would rather make a new character from scratch I won't stop them. I'd probably arrange for some way for their gear to be recoverable, at least partially. If the decker gets kidnapped, I'm not saying the KE stop on his cyberdeck just for the lulz.
But, just because a character gets to a lowest point, I don't think you should just ditch him. If you've been playing for a while, and the group is established, your allies should help you recover your losses (they bothered to break your ass out of jail in the first place) and the character would likely experience some interesting growth. Put him in debt to some powerful people, maybe. Maybe the group is stuck playing Company Man for a while to pay off some loans. Be creative! Don't just say "I lost my shit? Fuck this. New PC." The GM should be willing to work with you on this.
Perhaps. While I agree that playing "gotcha" with burning Edge would be poor form, sometimes chars die. Even in dnd, if your char falls in a volcano that's it. No body, no rez. My point isn't: GMs have other ways of messing with players who burn Edge, so much as it's: burning Edge doesn't unilaterally mean that you get to keep playing that char. There are extenuating circumstances outside the Condition Monitor.
Well, for one, True Resurrection. You don't need the body for that. But more to the point, I do consider PC death to be in the hands of the player as long as they have a point of Edge. See, I don't think PC death has to be included for a game to be good or for there to be tangible risk. Reputation, wealth, and other things play in enough. Just like how you can watch and get invested in a TV show, even though you
know the hero isn't going to just die any time soon.
As for "what about the guy in prison"? I'd involve him. I'd either be playing out his time in prison (TV shows have made this work before) as he stays alive and deals with prison politics while he uses what little communication with the outside he's given to wait for escape, or I'd actively involve him in the escape process, giving him objectives and things he needs to set up from the inside.
Now, I'm not saying all this work and effort needs to happen every time a player goes down. That would be... Awful. But, I'm not going to tell a player who really wants to keep his character "Nope, burning the Edge does nothing." We'll use the rules in the book and come to a conclusion that works for the game and the player.
EDIT: ZombieAcePilot and MijRai's ideas are right on point. Shadowrun is a world run by manipulators-- Not destroyers. Runners are (deniable) assets, and having one by the short hairs is a great opportunity.
PCs failing shouldn't just be an end, with a pop-up "MISSION FAILED" screen and sad music. It's a jumping off point for
consequences that the characters have to deal with. It's got great creative potential. To just have a PC die is the loss of a story.