Short answer. Yes. Under Article 878, a disposition with a suspensive term does not stop the instituted heir from acquiring his rights and passing them to his own heirs even before the term arrives. So if he dies while merely waiting for the date, his heirs step into his place and receive the inheritance when the term comes.
What the law says
A disposition with a suspensive term does not prevent the instituted heir from acquiring his rights and transmitting them to his heirs even before the arrival of the term
Civil Code, Article 878 — Dispositions With a Suspensive Term. Read the full provision →
A term postpones enjoyment, not the right itself
A suspensive term is simply a future date that must arrive before the heir can actually take or enjoy what was left to him — for example, "my house passes to Pedro five years after my death." Article 878 makes clear that A disposition with a suspensive term does not prevent the instituted heir from acquiring his rights and transmitting them to his heirs even before the arrival of the term. The heir's right vests at the testator's death. What waits is only the moment of delivery and enjoyment. The right itself is already his property from the start, held in suspense until the calendar catches up.
Because the right vests, it passes on his death
Since the instituted heir owns the right the instant the testator dies, that right forms part of his own estate. If he then dies before the appointed date, he does not lose it and it does not return to the testator's other heirs. It is transmitted to his own heirs exactly like any other asset he held. They inherit his position and, when the term finally arrives, they receive the property in his stead. The intervening death does not defeat the gift; it merely changes who ultimately collects on the date the testator chose.
A term is not the same as a condition
This rule is specific to a term — an event certain to happen, such as a date. It does not govern a true condition, which depends on an uncertain event that may never occur. Where a gift is conditioned on something that might not happen, the heir acquires no vested right until the condition is fulfilled, and premature death can change the outcome. So before assuming the heirs inherit, read the will carefully to see whether the testator fixed a date that must come, or attached an uncertain requirement. Only the former carries the transmission this article describes.
What this means in practice
In practice, the estate is settled at death, but property tied to a suspensive term is held — usually by the executor or the other heirs — until the date arrives, then handed over to whoever is entitled by then. If the named heir has died, his heirs prove their relationship and claim in his place. Disputes usually turn on characterising the clause correctly and on identifying the heir's own successors. The article protects the family of an heir who simply did not live long enough to see the date the testator set, keeping the gift within his bloodline rather than diverting it.