More is needed. Also, I assume you meant before the testator dies not before the testator executes the document. Also, what does the document about the gift, how is wording of the gift? Please provide that language and it will be easier to give you a complete answer.
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Attorney Shultz is correct. Without reviewing the will, it is impossible to know what happens if one of the three beneficiaries dies prior to a parent's death. With that said, in my documents, I use the term "to my descendants who survive me, per stirpes." Under Connecticut law (in your scenario), that language leaves the assets 1/3-1/3-1/3, but if one of the children dies, then his or her 1/3 share goes to his or her children, if any. If the deceased child has no children, the 1/3 share reverts to his or her siblings. Any questions with respect to this document should be referred to an experienced estate planning lawyer in the jurisdiction where the parent is residing. Good luck to you.
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It is necessary to review the language in the will to determine what happens to the deceased beneficiaries share. That language controls over any law and without seeing the will, it is impossible to answer your question. It is well worth it have a consultation with an attorney and get some direction.