Happens all the time. You politely and firmly inform them that they may not sit in that seat and tell them to return to seat they have paid for.
I don't understand this mentality at all. Would you walk into a supermarket, pay for a carton of eggs then march back in and help yourself to cheese, milk and bread without paying for it? No, because you know it is called stealing.
Just because a seat on an airplane is unoccupied doesn't mean it belongs to you. It belongs to the airline and it's not for you to decide what will happen to it. A business class\first class seat is a product, the same as cheese in your supermarket. Having that seat empty if it hasn't been sold is worth quite a lot to the airline and to everyone else who has paid for the experience of sitting in that section. If you had just paid 400% more than everyone else on that plane you would not want someone on an economy fare sitting next to you.
If you want caviar then pay for it. If you'd rather pay less than enjoy the experience that you have paid for, which includes middle seats, less legroom and a full cabin.
I do not see someone upgrading themselves as fun and cheeky. I see them as someone who is not prepared to pay for the experience and is therefore entitled only to the economy seat they have paid for.