Interesting idea! I could add something like this as an optional feature when starting a new game. I know quite a few people want the game to be a sandbox without any game over screens, & I'm keen to preserve that wherever possible. But I'm also happy to add this kind of thing as a toggleable extra.
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Fairy nuff
Other ideas hat could lead to a "Ending state"
Fattening up too many of the Gentle Meadows staff, meaning they can't hire anyone else leading to you becoming a full time feeder / carer to everyone in the facility
Getting too many still mobile people addicted to Dizzy's Doughnuts at the same time meaning that nobody in town is doing anything but eating, and filling your pockets while everything else shuts down around you.
Loosing too much weight (or dropping down to skinny multiple times) while in a relationship with a feeder, so that rather than dropping you to the curb, they decide that you can't be trusted with your own weight because you keep making poor decisions so they kidnap you and fatten you for the rest of your days.
Getting stuck / becoming immobile while out on a day trip, and winding up as a tourist attraction as the bottomless gullet.