I wondered about that as well. He mentions other part-time gigs he did/is doing. Aren't you supposed to lose benefits if you are working at anything? Maybe there is loophole for part time.
I thought of another thing he can do: substitute teaching. He says he wants to be a teacher, subbing is great way to break into a full-time teaching job.
RE: On his website he has a whole list of books he has reviewed there. Doesn’t look unemployed to me, unless they don’t pay you at the Daily Beast (aka Newsweak).
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If he was receiving unemployment checks while simulataneously receiving pay from his book reviewing, this is grounds for fraud... just saying.