Short answer. Not automatically ruled out. Article 172 makes the Fund liable to the employee or his dependents, except where the death was occasioned by a wilful intention to injure or kill himself. That exception has to be established; the manner of death alone does not decide it.
What the law says
willful intention to injure or kill himself or another
Labor Code, Article 172 — Limits On Fund’s Liability. Read the full provision →
The article speaks to dependents directly
It is worth noticing at the outset that the provision makes the Fund liable for compensation to the employee or his dependents. A death claim is therefore not a claim you are pursuing on the deceased's behalf as a matter of courtesy; the family's entitlement is written into the article itself. That is the starting position, and the exceptions that follow are subtractions from it. Nothing in the provision requires a family in your situation to justify making the claim at all.
Wilful intention is the whole of the exception
The words are wilful intention to injure or kill himself. Both carry weight. The exception is not framed around how a death looked, or around a coroner's classification, but around an intention that has to be shown to have existed. That distinction is not a technicality. Deaths that appear self-inflicted are not always so, and a person's capacity to form and hold such an intention can itself be in question where illness, medication or acute distress was involved. Those are matters of evidence, not assumptions to be drawn from the circumstances.
Occasioned by, again
As with the other exceptions in the same sentence, the link required is that the death was occasioned by the wilful intention. So the exception is directed at a death that the intention brought about. A denial that reasons backwards — from the fact of the death to the existence of the intention — has not done the work the article requires. Where a claim has been refused on this basis, the useful question to put is what the finding of intention rested on, separately from the finding about how death occurred.
What a family can do next
This is a difficult thing to have to attend to, and it helps to keep it to a short list. Get any denial in writing, and note precisely which exception it invokes. Keep the death certificate, medical and hospital records, any treatment history for illness in the period before, and any investigation or police report. Keep the employment records too — contract, payslips, contribution records — since the family's standing as dependents and the deceased's coverage are separate matters from the exception. Take those to a lawyer rather than deciding on your own that the claim is closed.