When I sell something, the part is not marked as sold until I see the money, and that would be the full amount. If someone wanted to buy something I had for sale, and they want to pay via a mail MO, that would be fine but the MO would need to go on the mail the next day at the latest. Part of the agreement is if I did not receive the MO by the agreed date, the part would be sold, if a second buyer stepped into the picture. That is fair to everyone.
For sellers that agree to take partial payments,, you are just enabling folks that are borderline able to make ends meet and do their hobby, make more poor decisions. Just say no.
Think about it. Are there any buyers that would be happy if the item they bought was delivered a piece at a time at a schedule convenient to the seller? No buyer would stand for that. So just don’t do that as a seller and the problem goes away.