I had guests leave a few things behind, nothing of much value. some I shipped, some they said they don't care, so I tossed them. Still, this is my personal "policy" about things left behind :
1.) no matter what it is, I message the guest as soon as I find the item, offering to send it, asking for shipping address.
2.) if it is an item easy to ship within the US, I do it as a curtesy to the guest, up to a cost of about $15-18. ( which is less than 10% of my minimum 2 night stay) . I think such curtesy without looking for reimbursement goes a long way in building trust and goodwill. I see it in relation to how much they spent for their stay. If shipping costs were higher than 10-15% of the stay, I would kindly ask for reimbursement by using Airbnb's platform for "request money".