What is the ruling on living in a house that the state bought from an original owner whom it did not compensate, then the state sold it to another buyer who built on it and lived in it, and then the original owner demanded compensation?

It is not permissible for anyone to seize another's property without right. If the state seizes land and does not compensate its owner, this is considered usurpation. It is not permissible to purchase anything that has been usurped, as this falls under aiding in sin and aggression and devouring people's wealth by false means. The purchase of usurped property does not transfer ownership from its original owner. If the buyer knows that it is usurped, he is not permitted to use it because the sale is invalid. The obligation is to return the land to its owner and demand the price from the usurper.