Maybe he was hoping that even if he was to die his mother would still get the money for the medicine?
Rei mainly relies on her knowledge from the game and probably didn't inherit the memories of the original Rei. So for her there was no emotional attachment to him as a person, just the knowledge that he's supposed to be the MC's childhood friend. She has a clear agenda - keeping Claire save - and is willing to use her knowledge from the game to manipulate the story, treating the characters that she isn't already close with as chess pieces.
Claire on the other hand is a sheltered young lady raised as a part of the ruling class. Her "villainess" status came from her ignorance towards the situation of the lower class and being too stubborn to change her views, not from being a cruel asshole. Right now is the first time she's being confronted with the reality of poverty, so everything is still fresh and raw for her. Both Rei and Misha on the other hand are aware of tragedies like this happening all over the place so they are probably somewhat desensitized and prioritize the immediate danger