Short answer. Yes — but as a depositary, not a pledgee. Article 2111 says the pledgee's written renunciation of the pledge extinguishes it, without needing your acceptance or the return of the thing. The security is gone, yet he keeps your item and becomes a depositary, so he must still safeguard it and give it back.
What the law says
A statement in writing by the pledgee that he renounces or abandons the pledge is sufficient to extinguish the pledge.
Civil Code, Article 2111 — Abandonment of the Pledge. Read the full provision →
What the law says
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 ends, the duty does not
Article 2111 says that a statement in writing by the pledgee that he renounces or abandons the pledge is sufficient to extinguish the pledge. The written renunciation does the work by itself: neither the acceptance by the pledgor or owner, nor the return of the thing pledged is necessary. So the security relationship is over the moment the pledgee puts his abandonment in writing. What matters for your question is the last clause — the pledgee, the article says, becomes a depositary. He no longer holds your item as security for a debt, but he still holds it, and the law recharacterises the reason he holds it.
What being a depositary means
Once the pledgee becomes a depositary, he holds your thing for safekeeping and must return it to you. A depositary's core obligation is to keep the thing and give it back to the owner on demand, taking care of it in the meantime. So abandoning the pledge does not free the lender to be careless with your item or to treat it as his own; if anything, his duty is now squarely about custody and safe return rather than security. If the item is lost or damaged through his fault while he holds it as a depositary, he can be answerable for that, just as any depositary would be.
Why abandonment does not release the item
It helps to see what the pledge was and was not. The pledge gave the lender the right to hold your property and, in case of default, to have the thing sold to satisfy the debt. Renouncing the pledge surrenders that security right — but it says nothing about ownership. The item was always yours; the pledgee only ever held it. So when the security disappears, the thing does not revert to no one, and it does not become the lender's. He continues to hold property that belongs to you, and the law names that relationship for what it now is: a deposit.
Getting your item back
Practically, a written abandonment strengthens your hand. You no longer have to redeem the pledge to recover your property, because there is no longer a pledge securing anything; you are simply an owner asking a depositary to return what is yours. It is worth keeping the pledgee's written renunciation, since it is the document that ended the security and fixed his new role. If a debt remains between you, that debt still exists — abandoning the pledge lets go of the security, not of the underlying obligation, which the lender may still pursue by ordinary means.