Personally, I would cancel and refund, then issue an invoice for full payment. I would not accept partial payments for various reasons. First, we have credit cards for buyers who don't ahve the cash right now.
Second, if the buyer doesn't have sufficient funds, why do think this is a reputable buyer and not a buyer?
Third, you will have the item shipping associated with only one of the payments, creating serious issus in case of a dispute. You will also have one transaction with no shipping assocated, allowing a buyer to claim non-delivery and get a full refund for that part.
There is no logical reason to split a payment in 2 for a single item without creating significant risk of loss for your business.
