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Within the last year a good friend of mine was widowed. She is 55 and her husband died of a heart attack at age 58. They have two children both in college.
A few months after the husband died, his mother passed away. Now the mother had cash and assets in the multi-millions (I'm not sure exactly how much, my friend didn't specify and I wasn't going to pry).
My friend was surprised to learn that the money her husband would have gotten if he had outlived his mother was going to pass directly to the two children and she got nothing. (This after 30 years of marriage). So her children will be well-fixed and she will have only her husband's life insurance and their small savings.
My parent's will is the same way. It says that if I predecease them, my share goes to my children. My husband's mothers will is written the same way. I think it's probably standard boilerplate will language. (Even though the child that died before his parent would likely want his spouse to be provided for with the inheritance he didn't live to collect.)
As an old woman in my family says "Money always follows the blood" meaning unless you share DNA you are cut out.
I don't know what I'll do when my children marry. But I think that if they have spouses that are good people, long marriages and getting older, I'd likely leave them a portion.