Ownership does not transfer to a new tenant simply because it was left. "Abandoned" is your term and you have provided no case law/statutory authority to back that up. Two theories, Landlord -Tenant law surely does not assign any left property to a new tenant. Second, it may be the property of the cable business to use by the subscriber. Therefore you risk taking their property, not the tenant's.Do I have any legal obligation to give it back to him? Is it his fault for choosing to leave items behind when he moved out? Is the landlord at fault for not making sure the item was properly "abandoned?"
It may well be "technically/legally" abandoned, but that is a presumption on our part. If forgotten, I would classify it as "Mislaid" property. Too many variants to conclude you are actually right.