Hello
We were in a rush to get to our next stop, and realized 6 hours after we left an Airbnb house that we had left a few items behind, including a reading lamp and bedding. Contacted the host who claimed he threw the items in the trash and declared that we should not have "abandoned these items". This was 6 hours after we left the place, the same day! We highly doubt He threw them away, we suspect he decided to keep them.
After 24 hours, he added that he is keeping the items because the place 'was a mess", which was not true. Mind you, there was water out front from leaking hoses, and a pile of leaves we had to walk over to get to the door.
Long story short, Airbnb is not doing anything to help us. So although host is supposed to contact you if you leave items behind, it seems legal by the rules of this site that the said host could decide to keep everything or trash it. And you have no recourse, because there is no penalty for the host to do so.