Short answer. Not on your own decision. The item you pledged is security for the debt, not payment of it, so walking away and leaving it with the creditor does not cancel what you owe. Only the creditor can accept the thing as payment, and only the creditor can give up the pledge.
What the law says
A statement in writing by the pledgee that he renounces or abandons the pledge is sufficient to extinguish the pledge. For this purpose, neither the acceptance by the pledgor or owner, nor the return of the thing pledged is necessary, the pledgee becoming a depositary.
Civil Code, Article 2111 — Abandonment of the Pledge. Read the full provision →
The pledge and the debt are two different things
When you pawn or pledge an item you make two commitments, not one. The first is the debt itself. The second is the pledge, which merely gives the creditor a thing he can sell if you do not pay. Surrendering the item satisfies the second and leaves the first untouched, so the creditor may keep the item as security and still sue you for the full amount. This surprises many people, because the whole point of handing something over felt like paying. It is not payment; it is collateral. Until the creditor agrees otherwise or the thing is actually sold under the rules for pledges, the balance stays on your account.
What the article really governs
Read closely, this provision is about the creditor letting go, not the debtor. A pledgee — the person holding your item as security — can end the pledge by a written statement that he renounces or abandons it. He does not need your agreement, and he does not even have to hand the item back for the renunciation to take effect. What changes is his character: he stops being a creditor holding security and becomes a depositary, someone simply keeping your property. He must then take care of it and give it back when you ask. Your debt, meanwhile, survives untouched. He has given up his security, not his claim.
The route that does work: getting the creditor to accept the thing
Property can be handed over in settlement of a debt, but it takes the creditor's consent. That arrangement is treated in law as a sale of the thing applied against what you owe, and the essential point is that both sides have to agree on it — including whether it wipes out the whole balance or only part. Put it in writing, state expressly how much of the debt it extinguishes, and keep a signed copy. A verbal understanding that the pawnshop or lender would just keep the item is exactly the arrangement that later turns into a collection suit for the entire amount plus interest.
If the item is sold at auction instead
There is one situation where losing the item does end the debt. If the creditor forecloses the pledge and the thing is sold at public auction under the rules governing pledges, the principal obligation is treated as extinguished by that sale — even where the proceeds fall short of the balance, and the creditor is not entitled to chase you for the shortfall. This is a real difference between a pledge and other kinds of security, so it is worth knowing which one you actually signed. The auction is the creditor's remedy, though, not a step you can trigger yourself by refusing to pay.