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North Carolina has a fund to compensate people who've been falsey imprisoned. I can think of two cases - both men imprisoned for several years for rapes/murders they did not commit - where this fund was used. It's not a lot of money, but IIRC state law allows falsely convicted people to sue the state or local governments for damages as well.
However, I don't know if this applies to the Duke students because they were never convicted of anything. They may be able to at least recover some of their legal debt in a civil suit if they can prove that the police or DA's office acted improperly.