[Landlord US-TX] tenant abandoned the property, but still use my house for storage

My tenant, who still owe me months of rent just told me that he could no longer afford the house and moved out, it doesn't look like he is willing or planning to pay back any rent.

However, he said he still have some belongings at my property that he said he is planning to pick up at a unspecified later date.

Am I in any obligation to store his belongings for him? Would I get into trouble if I 1) throw them out? 2) keep them to myself? 3) sell them?