In British English there are a number of idioms which capture the idea, in addition to Graham's excellent answer.
A person who has given up is somone who can't be bothered to make the effort, she's just let herself go.
- Wow, she's really given up
- She just doesn't make the effort any more.
- She really can't be bothered, can she?
- She's really let herself go, hasn't she?