When he was let go from his temporary contract, he should have filed for unemployment. If he did so, and they were not tax payers, he was classified as a contractor, not an employee, then he would not have been eligible. If he was a regular full time employee of a tax paying entity (almost ,everyone except certain religious organizations) he would have been eligible, even though the jobs were termed "temporary," or were funded year to year. Even governmental entities have to pay unemployment taxes.
If he didn't file, because he was under the mistaken impression he was not going to be eligible, then he probably has missed his chance, depending on how long it has been since he was laid off. So at this point, the question of whether he was eligible when he was laid off is not relevant. Whether or not he has found work has no bearing on his unemployment status. Whether he had worked for a covered employer is the key. If he files now, he MIGHT have some quarters of work left, depending on how long it was since he was laid off last year. So I'd request that he file, and show you the paperwork that says he's not eligible. The fact he was a temporary employee wouldn't keep him from being eligibile. It is not a welfare program, either, so if he's not signing up due to pride, make him. He needs to be drawing, and paying a percentage of that money to you though unemployment in Florida isn't very much a week. It is certainly something.