This didn't happen to me, but a friend, but I'm curious myself.
Note this is US-specific, as I understand unemployment insurance works differently in the US compared to other countries. My and my friend both live in WA state where I understand unemployment insurance is operated by the state government, but still considered private insurance, and so doesn't constitute any kind of welfare.
Said friend was fired for poor performance recently (I believe his manangement/HR was looking for excuses, but I digress). He only has a few weeks' expenses saved up (messey divorce) so I told him to apply for WA's generous unemployment scheme (it's like $600/week, tax free!), however he was hesitant.
His reasoning for not submitting the paperwork was his concern that a future potential employer would hire a background check company and they would somehow be able to find his unemployment claims and not move to make him an offer, deeming an unemployed new hire less valuable than someone already with a job looking to switch (he's trying to get a job ASAP so he can make it look like he's switching employers and hide the fact he was fired - his previous employer has a HR policy of never disclosing the reason someone was terminated or resigned).
(He isn't planning on lying or defrauding a future employer - he plans to just say that "he left the company to pursue new job leads" - but he's convinced if they knew he collected unemployment then they would write him off)
I told him not to worry and pointed him to WA's law on unemployment information confidentiality includes a $5000 penalty for unauthorised use of unemployment records - but the law isn't precise about what constitutes unauthorised use. The law does mention that inquiries for investigations are allowed - so would an ordinary background check then be able to include this information?
Is he being paranoid, or reasonable, in his suspicions and reservations?