Short answer. Generally no. Article 1287 says compensation cannot be set up against a creditor who has a claim for support due by gratuitous title. So the one who owes you support cannot simply cancel it by pointing to a debt you owe him. Support is protected because you need it to live.
What the law says
Neither can compensation be set up against a creditor who has a claim for support due by gratuitous title
Civil Code, Article 1287 — Debts Excluded From Compensation (Deposit, Support). Read the full provision →
What compensation is, and why support is shielded
Compensation, or set-off, is the way two people who owe each other money can cancel their debts to the extent they overlap, so that only the balance is paid. It is convenient, but the law refuses to let it apply to certain obligations. Article 1287 says neither can compensation be set up against a creditor who has a claim for support due by gratuitous title. Support means the money a person needs for food, shelter, clothing, medical care and the other essentials of living. Because a person's very subsistence depends on it, the law will not let that lifeline be wiped out by offsetting it against some unrelated debt the supported person happens to owe.
Support 'due by gratuitous title'
The protection covers support that is due by gratuitous title — support the law itself, or a pure act of liberality, obliges someone to give, such as support owed within a family. This is the classic protected case. The reason for the qualification is that when support is granted for free, out of duty or generosity, offsetting it would defeat the whole purpose of ensuring the recipient can survive. Article 1287 also bars compensation where a debt arises from a depositum or from the obligations of a depositary or a bailee in commodatum, treating those trust-based duties, like support, as too important to be quietly cancelled out by set-off.
The narrow exception and what it does not cover
The rule is not completely absolute. Article 1287 protects support, subject only to one narrow exception the Civil Code separately preserves within its own rules on support. That reservation, however, is narrow; it does not open the door to a debtor of support freely cancelling current support against ordinary debts. The practical takeaway is that the person owing you support generally cannot stop paying by invoking a claim that you owe him money. He must pursue that claim through the proper means, while continuing to provide the support you are entitled to. The two obligations are kept separate precisely so your basic needs are not held hostage to a dispute.