I hate pop-unders (background popups, whatever you want to call them) with a passion. When a website I visit spawns one, I immediately blacklist the entire domain. It's a losing battle through.
I can't think of a single good use-case for pop-unders (or pop-ups even)
When you do a captive portal with some sort of timer (hotel, airplane, etc), they will sometimes do a pop under with a timer that has the option to pay more to renew. That can be slightly useful.
Or when you visit a site, and it does a pop under of a survey about that site. Then you see it when you close the window and maybe fill out the survey. That one is less useful but at least legit.