Short answer. No. Under Article 1939 of the Civil Code, a commodatum is purely personal in character, and the death of the borrower extinguishes the contract immediately. The right to use the equipment does not pass to his heirs. They must return your property, not continue the loan.
What the law says
Commodatum is purely personal in character. Consequently: (1) The death of either the bailor or the bailee extinguishes the contract
Civil Code, Article 1939 — Commodatum Is Personal. Read the full provision →
The personal character of commodatum
A commodatum is not just a contract about a thing — it is a contract built around a specific person. Article 1939 states plainly: Commodatum is purely personal in character. The bailor agreed to lend to that particular person, not to whoever that person's estate happens to pass to. This is why the law treats the borrower's identity as essential to the deal, not incidental to it. When that person dies, the basis of the arrangement disappears with him.
Death of the borrower ends the contract
The Civil Code is direct: the death of either the bailor or the bailee extinguishes the contract. This means the moment your borrower passed away, the commodatum ended — not at the close of the month, not when his estate is settled, but immediately upon death. The surviving heirs acquire no right to continue using the equipment. They step into their decedent's estate, yes, but the right to use your property under the commodatum never formed part of that estate in the first place, precisely because it was personal to him.
What the heirs must do
Once the borrower dies, the heirs are obligated to return the thing to you. They hold it without any legal basis to continue using it. If they refuse, or delay without good reason, they could be held liable for any resulting damage or loss. You are well within your rights to demand return of your equipment promptly. If the estate is going through settlement proceedings, you may need to present your claim as a creditor of the estate — not in the sense of a money debt, but in the sense of a demand for the return of your property.
Note: your own death would also end it
The rule cuts both ways. If you, the lender, were to die during the loan period, the contract likewise terminates. Your heirs would have the right to demand return of the equipment from the borrower, even if the agreed period had not yet lapsed. Neither side's heirs can be bound by a contract built on the personal trust between the original parties. This mutual extinguishment on death is what makes commodatum fundamentally different from a lease, which ordinarily binds the heirs of both parties.