The absurd end of this spectrum is what happens when police damage a random persons property while chasing a suspect. They’re generally not liable for it, however most homeowners insurance won’t cover it.
I remember an early GoFundMe from a lady that went to work and a guy broke into her house and had a shootout with the police. She came home to being homeless (house got condemned because plumbing, gas, etc is bullet-riddled), and it’s a really disconcerting story to hear. I don’t recall if the city settled to quiet the story down or not.