For private sector: of course, since they can simply file for bankruptcy or use other diversionary tactics. For government or singular public entities, clearly this can't be the case. If the government is dismantled because an individual member creates intentional trouble, we probably would live in chaos real quick. Similarly, if you set up a public university (or a public library for example), it would not be very useful or fair to the public if they can no longer enjoy the services by the wrongdoing of a single individual.
This is a rather depressing way at looking at suits, but I doubt it is accurate.
You can sue the government, just not for copyright it appears. I was actually photographing the Cathedral of Bryn Athyn a few years back, which is owned by the Pitcairns (actually the entire town of Bryn Athyn is owned by the Pitcairns). One of the sons is a rather brilliant engineer and invented something for use on military helicopters. The US military stole the technology and the son sued them for it. It was an extremely expensive suit and the military thought there was not way he would be able to afford it, which is why they did not settle, but they knew little of the family. They are wealthier than God, and he eventually won. However, most people would not have the wherewithal to do so and is probably more the reason why it does not happen often.
(Most) Can't Fight City Hall!