I could definitely be wrong, but my understanding is that when unemployment benefits run out, so does one's status as unemployed, since they've lost the point of contact that enables them to ask those questions.

At least twice in the last decade, he's been unemployed so long his benefits ran out. Perhaps the label in that case isn't "retired," but he wasn't counted as unemployed, either.

Number of unemployment insurance claims is sometimes cited as an economic indicator, but it's definitely not the main measure of unemployment.

The BLS tracks six measures of unemployment rate via survey called U1-U6. U3 is the official unemployment rate, but they report the others as well[1].

For U3, you are considered unemployed if you do not have a job, have actively looked for work in the prior 4 weeks, and are currently available for work. U4 is that plus anyone who wants a job, but gave up looking because they don't think they will find one. U6 adds in people who only have part-time work but want full-time work.

[1] https://en.wikipedia.org/wiki/Unemployment#United_States_Bur...

[2] https://www.bls.gov/cps/cps_htgm.htm#unemployed

Check out the link in my reply above, it's pretty interesting. It lays out exactly how they collect the unemployment statistics and calls out that they can't use unemployment insurance numbers for the exact reason you said - benefits run out, but people are still looking for work.

They basically survey 60,000 people and ask a specific set of questions to figure out which "bucket" people are in.

U-3 does not exclude those whose benefits have run out but are still actively looking for work. It relies on social insurance claims in part, but also uses surveys to estimate how many folks are looking for work that aren’t receiving unemployment.