Taking a look in the gear_medical config, it doesn't look like any checks are made to see if players actually have any blood to take. Pretty interesting. Definitely exploitable if that's the case.

I've taken blood from an unconscious player and it killed them.

A reason why this happened to your friend is that he had more than a 1000 blood before you took blood from him which is why he didn't die immediately after doing so.

He had to have been suffering from high shock so he was still unconscious, after you took the blood he would remain unconscious while recovering from his shock but remain unconscious until you gave him back his blood.

So he would have probably recovered faster if you left him alone