Haha, okay challenge accepted! There's this old computer game called 'Hotel 626'. It’s not available anymore but you can find gameplay vids online. It was supposedly only playable from 6 pm to 6 am and it messes with your head, can send you actual texts and calls during the game. …

Although not exactly high-profile, 'Special Unit 2' fits your description. Mid-2000s, under-the-radar show about a Chicago cop dealing with supernatural beings which they referred to as 'Links', and yes, locking them up was a thing. Mostly forgotten, but had a cult following. Worth checking out?