Can someone explain marriage and ssi benefits to me?

my friend has a disability since birth. she lives with her fiance and their 2 kids. She was telling me earlier that if they were to get married she would lose her ssi check. Is that true? can they just take it away?It's not like getting married will take her cerebral palsy away. My question 2 her was how in the eyes of the state would a marriage license affect her check? but the state doesnt care if they live together? weird.. I also said can't she just change her last name so it's the same as her children?