This is foundational to American legal system in many cases. If your local cops for instance unjustly beat say Cubans and get sued for it the inhabitants will pay and possibly even their children through debt.

Well, that's how it should work. Qualified immunity massively complicates this in favor of the cop and therefore the city employing said cop and the residents of the city. It is technically not impossible to win such a case if you get a court to take it, but you might be facing some insurmountable odds getting a court to take the case.