It is true that anyone can sue anyone for anything. That doesn't mean you'll win. Based on the information in your post, you would lose.
It doesn't matter if she actually defrauded them or not; if they BELIEVE she did, they are legally allowed to fire her. Even if they are mistaken and she didn't defraud a thing.
You do not have a wrongful termination case based on the facts of your post.
As for a slander case, in order to have a case for slander, the burden of proof would be on you to prove ALL of the following:
First, that what they said was FALSE. In other words, that they KNEW she hadn't committed fraud but said so anyway. You don't have a suit for slander if they misunderstood. YOU have to prove that they deliberately accused her of committing fraud, KNOWING that she had not.
Second, that they broadcast this to an audience. It's not enough for them to say it to her; they have to have said it to someone else, who is not a "party in interest" to the situation. In other words, it's not enough for them to have said it to her supervisor, or someone in HR. YOU have to prove that they told someone totally unconnected with the situation, that she committed fraud. If they didn't, it's not slander.
Third, that as a direct result of their telling this hypothetical third person about the alleged fraud, she suffered damages. YOU have to prove that BECAUSE they told SOMEONE ELSE that she committed fraud, she lost the chance at a new job or in some other way was damaged.
The company doesn't have to prove a thing in this case. Are you prepared to spend money on a lawyer to prove all of the above?
As to whether or not you can claim unemployment, that depends on the laws of your state. However, in the large majority of cases, they're not going to pay you to quit a job. If you'd stayed on the job and claimed partial benefits because your hours were cut, in many states you'd have qualified. But since you quit, thus ensuring that you had NO pay instead of SOME pay, in most states you will NOT be able to get unemployment at all. You can file a claim and see what happens, but the likelihood is that you'll be denied.