My daughter told me she had a conversation the other day with a colleague who keeps a worm farm in her house because she's fascinated by them. The woman in question had a scientific interest in worms. I can't see them being great pets, but.
I culture small white worms, related to the type you'd find flipping over a summertime rock in Canada. I have 5 small boxes in a cool spot under a tank, and I use the worms to prepare fish for breeding. I guess that qualifies as a worm farm.
A photo would show tiny worms on wet scrubber sponges with kitten food, and petrie dishes to climb out and get caught on. Not a great visual...