If they paid her like it's a regular job then unemployment taxes come out of it. It's part of what comes out of all of our checks each pay period and where the money for the program comes. At least that's always been my understanding.
I don't see how FL can keep it to only FL DL's though. Between seasonal workers due to those that hold residences elsewhere and college students not to mention military spouses, there's plenty of people all over the country that are legally in the state with a different DL. Or I went to CA for 4 years with my WA license and shouldn't have, but I wasn't a CA resident, paid out of state tuition and still voted in WA, my car was plated in WA etc.
You also can't get unemployment if you quit and it wouldn't matter if where she was previously working isn't open, she wasn't an employee for there for a long enough time. It doesn't matter that if she'd still have been there x would happen because she wasn't there.
I think more of the conern would be how close are they looking at it and how do they look at college program kids. Even if it's considered a paid internship they are paid like it's a pt job not with a stipend so taxes and SSI etc should have been taken out. If they weren't I'd be concerned about a lot of kids taxes since the program started