If my husband was laid off and given a final settlement/adjustment to cover unused PTO but his company now says it made a mistake, can it take it back? 

It depends by what is made by a "mistake":

1) If there was an agreement as to what he should receive, and they accidentally paid him more than that (or paid him for something there was no agreement to pay him for), they may get the extra or excess back.

2) If they agreed to pay him for his unused PTO, but then later changed their mind or thought better of it, they may not recover it--they have to stand by the agreement made with him, even if they wish they had not agreed to that (or even if someone realized that he or she violated company guidelines or his/her own boss's instructions in making that agreement).