I'd suggest that even if your parents can't do it, that you put up clear boundaries with your sister. You will not make her food or go to the store for her. You will no longer listen to her relationship problems. If she wants to hang out or talk about other things or if she'd like help looking for a job, you can tell her you will help, but that you will not tolerate the other behaviour.

If you can set clear boundaries, maybe your parents can follow suit by your example.

Maybe suggest to your sister that she go and talk to a therapist if the relationships are so upsetting that she has to talk about them so much.