Short answer. No. Abandoning the thing does not settle anybody's account. The Code says so expressly about the lender, who cannot dump the item on the borrower to avoid expenses or damages, and the same logic leaves the borrower liable for damage his own fault caused.
What the law says
The bailor cannot exempt himself from the payment of expenses or damages by abandoning the thing to the bailee.
Civil Code, Article 1952 — No Abandonment to Escape Liability. Read the full provision →
Read carefully, this rule binds the lender
The article is written against the bailor — the person who lent the thing out for free. It exists because a lender who suddenly finds he owes money to the borrower has an obvious temptation: to say keep it, we are even, and treat the item as full settlement. The Code closes that door. Handing over ownership of a borrowed item does not discharge the lender's own money obligations. If the sums involved happen to be smaller than the item is worth, that is the lender's problem; he can offer the thing in settlement, but the borrower is free to refuse and insist on being paid instead.
What the lender might owe in the first place
Two obligations sit behind this. The first concerns extraordinary expenses — the unforeseen ones needed for the thing's preservation, as opposed to the ordinary running costs of using it, which belong to the borrower. The second is set out in Art. 1951: a lender who knows of a flaw in the thing and says nothing answers for the damage the borrower suffers because of it. Someone who lends out a car with brakes he knows are failing is in that position. He cannot escape it by telling the injured borrower to keep the wreck.
The borrower cannot abandon his way out either
If you are the borrower, leaving the thing on the lender's doorstep or simply never collecting your side of the argument does not close the matter. A free loan of a thing carries a duty to return that same item, and abandonment is not return. You still answer for damage caused by your own fault, for using the thing for a purpose other than the one agreed, and for keeping it longer than allowed. Ordinary wear from the use that was actually agreed on is a different matter and is not charged to you. But whether you owe anything turns on how the damage happened, never on where the item ends up.
This is a rule about who absorbs a loss
Cases like this rarely involve anyone behaving badly. A borrowed generator breaks down; a lent motorcycle needs repairs neither side foresaw. Both people are out of pocket and both feel hard done by. The Code's answer is to separate the questions: the thing goes back to its owner because it was always his, and the money follows the reason the cost arose — the borrower's fault, the lender's silence about a flaw, or an unforeseen need to preserve the thing. Sort out those two questions separately and in writing, with photographs and repair receipts, before either side starts talking about simply walking away.