don't let her take a few months off, keep her in the gym doing instructing for the "noobs" as much as you can. keep her in the game, keep her in shape with yoga, keep her motivated. if she comes back for the first time in a few months with an achey wrist and noodle arm then she probably will quit. it'll also set the example for caution for the rest of the students.
why was a long-term student not wearing the right gear? if she can't afford it then buy her a new gi perhaps, it is just about christmas. butter her up to keep her going but not out of guilt- and DON'T give her the belt because you feel sorry for her. if you poke at the issue a bit (she got her wrist broke from a silly mistake sparring, much less violent than the real deal) then she SHOULD be ready to show you a few moves by the time she's healed up (I'm not saying get her fuming mad but the occassional razzing will do).
please don't run a stinky class (my old one had people that wouldn't wash the gi's to keep them competitive by biohazard)