Sorry it took me a while to get back to this. Here's what I'm seeing:
When a beneficiary under a will dies before the testator, they gift to the predeceased beneficiary "lapses." As you have described it, your uncle left his entire estate to his mother. Perhaps anticipating that is mother would die before him, your uncle provided that, if his mother died first, his estate would go to his brother. However, it seems he did not provide what would happen if the brother died first.
Most, if not all, states have something called an anti-lapse law. Generally, that law provides that, if a beneficiary dies before the testator and the testator does not otherwise provide for the disposition of the gift to the predeceased beneficiary, the gift goes to the heirs of the beneficiary. Michigan's anti-lapse law is found in
MCL 700.2603. The unique thing about this law (at least I think it's unique) is that it only applies if the predeceased beneficiary "is a grandparent, a grandparent's descendant, or a stepchild of either the testator or the donor of a power of appointment exercised by the testator's will." Your uncle's brother is a descendant of your uncle's grandparents, so the anti-lapse law should apply such that the heirs of your uncle's brother. Since it sounds like the cousin mentioned in your original post is not a child (or otherwise an heir) of your uncle's brother, he'll be out of luck in terms of inheritance.
I don't really understand this explanation. Your cousin's frustration has nothing to do with how the law applies. Why do you not believe this? By the way, the concept of
per stirpes is of no relevance to this.
