Add parent as dependent while they are on Medicare

My parents are on Medicare and getting social security. Their age is 70+. If I add them on my tax return as dependents will they lose their benefits? My parents were saying since I would add them, govt might remove their benefits and I would need to add them to my insurance & take care of them. Is this true?

 

they don’t even file their returns since they have no income & not required to file.

 

also, if I trade stocks for & under my parents name (with their permission) will

that capital gain cause issues?