What happens in the case of a pre-deceased beneficiary under a Will?

Probably not.  Unless the wording for this is very unusual, it will mean that the share of the child who died without children of their own will go to the other child or children (or their own children, if pre-deceased).

If there were no surviving children (or grandchildren or great-grandchildren) at all, and nothing else in the will about that money (whether all or part of the estate), then it would be governed by the law of intestate succession (what happens when there's no will), and go to the surviving spouse.