If a person is visiting your home and goes thru your personal belongings ,tries to give away and or destroys or damages items, and tries to steel. Can this peron be prosecuted?

...and, could you imagine that some people who do this are actually cops? Then try to understand why most don't care that this happened to you, as truly awful as it is: which is why we need to re-think policing in our country, if not the world.

Of course! It's vandalsism, even thought they were invited inside-it doesn't mean they have the right to go thru your things nor destroy them. You will need proof that the belongings are yours and the proof that the items you own are being sold.