There's a man who's חייב מיתה by the kingdom. He's in jail waiting to be executed when he slips and falls and bashes his head on Shobbos. There a guards that could save him.
Do the guards have to save him on Shobbos (פיקוח נפש) or since he was a גברה קטילה (dead man walking) פיקוח נפש doesn't apply.
Please use sources.
This is addressed by Rashi's comments to Sanhedrin 72b. Rashi there says:
לפקח עליו את הגל - אם כשהיה חותר נפל עליו (את) הגל מפקחין עליו היכא דלא בא על עסקי נפשות אבל אם בא על עסקי נפשות כיון דניתן להרגו בלא התראה גברא קטילא הוא משעת (סתירה): If when the [ba bamachteres] was digging, the pile of stones fell on him, we clear it off him [on Shabbos] if he was not coming [with the intention] to kill the houseowner [if an altercation would occur]. But if he is coming [with the intention] to kill the houseowner [if an altercation would occur], when it would be permitted to kill him [the ba bamachteres] without warning, he is considered a "gavra keteilah" from the time of the entry [and may not be saved on Shabbos].
Rashi gives the reason that we don't clear the stones off of him as "because he is a dead man walking", as opposed to the reason of Rodef (likely because when buried under rocks, he isn't a rodef), showing that you wouldn't have to save a dead man walking on Shabbos.
(This is also the understanding of some acharonim, see here for example.)
