Even for those who don’t build their identity around their job, a lot of folks are just used to having something to do.
I work in retail, and I’ve had a surprising number of old folks ask if we have any part time jobs available - they’re not looking for steady paycheck, they’re looking for something to do two or three days a week. Even if your job isn’t necessarily who you are, it’s still a reason to get out of the house.
Some of them do… Or at least, they did - I mostly remember seeing it when I was in high school, and it sort of faded out when I was in college. Not sure if it fell out of style, or if it’s only a thing with the Hot Topic/mall goth crowd
Edit: uncorrected an accidental autocorrect