You've left me confused. If someone makes a will then (obviously) the executors carry out the instructions in that will.
If the will leaves something to a child of the testator, but that child pre-deceases him/her, then the bequest goes to the children of the intended beneficiary.
If the will leaves something to someone else who has pre-deceased the beneficiary (or to a child of the beneficiary who did not have their own children) then the bequest goes to the 'residuary beneficiary' if the will names one. Otherwise that bequest is treated as 'partial intestacy' and distributed according the rules of intestacy. (see below).
If there is no will then the intestacy rules apply to the whole estate:
http://www.wrighthassall.co.uk/media/article/attachments/Intestacy_flowchart_after_1.10.14_5_Aug_14.pdf