I have zero comment as to today's politics. And when in comes to broader policies, there are many different concerns at play.
I can refer you to likely the closest source material, though; assuming individual criminals and civilian life: Suppose a criminal is chasing after you with a gun saying you looked at me funny, I'm going to kill you!, and suddenly by pure chance an Acme anvil drops on him, injuring him and destroying the gun. Do you now treat his wounds?
Gemara Sanhedrin 72b
תנו רבנן (שמות כב) דמים לו בין בחול בין בשבת אין לו דמים בין בחול בין בשבת בשלמא אין לו דמים בין בחול בין בשבת איצטריך סלקא דעתך אמינא מידי דהוה אהרוגי בית דין דבשבת לא קטלינן קמ"ל דקטלינן אלא דמים לו בין בחול בין בשבת השתא בחול לא קטלינן ליה בשבת מבעיא אמר רב ששת לא נצרכא אלא לפקח עליו את הגל
[A burglar invading a house is usually assumed to be prepared to lethally silence the homeowner, and thus if the homeowner killed the burglar there would be a valid self-defense claim.] Our rabbis taught: if the burglar clearly was not prepared to use lethal force, you may not kill him, whether on Sabbath or weekday. If the burglar was prepared to use lethal force, you may kill him whether on Sabbath or weekday. In the case of self-defense, this teaches that although court executions are not performed on the Sabbath, one may kill in self-defense on the Sabbath. In the case of no self-defense, if I can't kill the intruder on a weekday, why would I think I can kill him on the Sabbath? Said Rav Sheishet: it means [you may not let him die, i.e.] you must save him from collapsed rubble.
Rashi explains: suppose I am 100% certain that this burglar is not prepared to kill me. As he's breaking into my house, he is severely injured. I am now obligated to save his life, breaking Shabbat if necessary, like any other person.
Whereas, says Rashi, suppose this is a burglar who comes with a gun and self-defense would apply, but while breaking into my house he is injured. I may not break Shabbat to save his life, says Rashi, as he was a dead man walking as soon as he broke in (because of my valid self-defense claim).
Rashi seems to be saying you can only break Shabbat to save a living person, not a "dead" person who is in danger of remaining that way. He does not say "don't save his life because he's a rodef", or "don't save his life because it's his fault", or anything like that. Which would imply it's permissible, and maybe even obligatory, to save his life on a weekday.
(This fits into a broader discussion of life-saving measures for those with legal status of "less-than-living", which may also include fetuses, someone undergoing a heart transplant, and someone in need of resuscitation. [E.g. the famous Tosafot how Elisha broke the rule of Kohen-don't-approach-a-corpse to save non-living Shunamite boy from remaining non-living "because he was sure resuscitation would work.])