If a person dies while the will is being settled, does the person's estate then benefit?

Other commenters are right. Look to the terms of the will. There may be a survival clause that says a beneficiary has to outlive the person who made the will by a certain amount of time. Or the will might state who would succeed if the beneficiary dies. Otherwise, in general, if a beneficiary dies before the executor has transferred the assets to them, the assets become part of the deceased beneficiary's estate. If the son had a will, the assets he inherited from his mother would be distributed according to the terms of his will. If he did not have a will, he died intestate and his heirs would inherit according to the laws of the state. If this is of direct concern to you and your interests, consult a trust and estate attorney.

His share will, in all likelihood, pass to his heirs.

That depends on how the will is written. Wills almost always elaborate on what happens. They will say things such as "If my son or daughter are deceased their portion of the estate should pass to their other siblings (names)" or If my son or daughter are deceased their estate should pass to their issue " and so on.
So basically you are down to read the will. If nothing is elaborated upon see a Trust and Estate Attorney (which you should have anyway) to discuss the rules as written for your particular state (they all vary).

This is very much dependent upon how the will is written and what the laws of inheritance in their state are.

Maybe....does the will specify that the beneficiary has to survive after the decedent for a certain length of time in order to inherit? I think the usual survival time required is 30 days, but it all depends on the wording of the will if any time at all is required.