Short answer. Yes. Article 2064 gives the guarantor of a guarantor the benefit of excussion against both the principal debtor and the guarantor he guaranteed. As a sub-guarantor you sit at the back of the line: the creditor must exhaust the debtor's property, then the main guarantor's, before reaching yours.
What the law says
The guarantor of a guarantor shall enjoy the benefit of excussion, both with respect to the guarantor and to the principal debtor
Civil Code, Article 2064 — Sub-Guarantor's Excussion. Read the full provision →
A sub-guarantor stands last in line
Guaranties can be stacked: a person may guarantee not the debtor directly but the guarantor, promising to answer if the guarantor himself cannot. Article 2064 places that sub-guarantor furthest from the debt: The guarantor of a guarantor shall enjoy the benefit of excussion, both with respect to the guarantor and to the principal debtor. He enjoys excussion twice over. Before his own property can be touched, the creditor must have exhausted the assets of the principal debtor and then those of the guarantor he backed. Being two steps removed from the original obligation, he is reached only when both levels ahead of him have run dry.
Excussion at both levels, not one
An ordinary guarantor's benefit of excussion runs against the debtor alone. The sub-guarantor's runs against two people, which is the whole point of the article. It is not enough for the creditor to show the debtor is insolvent; he must also pursue and exhaust the main guarantor's property, because that guarantor is the very person the sub-guarantor undertook to back. Only when the debtor cannot pay and the guarantor cannot make up the shortfall does the sub-guarantor's turn arrive. The double protection matches his double distance from the debt — he answers for the guarantor's default, which itself presupposes the debtor's.
What this does not change
The benefit is about order, not escape. Article 2064 does not free the sub-guarantor from liability; it fixes when that liability can be enforced. If both the debtor and the guarantor prove unable to satisfy the debt, the sub-guarantor still answers for what remains, up to what he undertook. Nor is the benefit self-executing at every level — like any excussion it has to be asserted properly and supported by pointing out available property of those ahead of you. It orders the queue in your favour; it does not remove you from the queue altogether.
Invoking it when the creditor comes to you
If a creditor turns to you as guarantor of the guarantor, the practical response is to require that both prior levels be pursued first, and to identify property they hold that can satisfy the debt. Establish that you guaranteed the guarantor rather than the debtor directly, since that is what brings Article 2064 into play, and insist the creditor exhaust the debtor and then the main guarantor before executing against you. Raised at the right moment and backed by pointing out reachable assets, the double benefit of excussion keeps your property untouched until everyone ahead of you has genuinely been drained.