If a son (heir w/ 1/4 interest in assets) dies before his father's estate closes what happens to his inheritence-father's will being probated in NY.

This looks like a NY law question, but generally you look at the terms of the Will for what happens if a beneficiary dies before distribution, and then to state law if the Will does not cover it.  In some cases, the bequest goes to the estate of the deceased person.  In other cases, the Will will provide for a successor beneficiary if the first beneficiary dies.  Sorry I can't answer this one.

As long as he survived his father, he (now his estate) is entitled to his 1/4 share.  Basically, that would be to whomever were designated as beneficiaries under his Will.  If he did not have a Will then he died intestate; in that case the intestacy laws of the state where he resided as of his death would apply.  Typically, to any wife and children; otherwise to parents, if living; if not to siblings.