If your parent's only income was Social Security they were not required to file a tax return---but it sounds like they already filed. If they did not say in MY INFO that they can be claimed as someone else's dependent, when you try to e-file with their SSN on your return as a dependent, your e-file will be rejected and you will have to file by mail this year.
Does your parent meet the criteria to be claimed as a qualifying relative?
Qualifying relative
When you add someone as a dependent, we'll ask a series of questions to make sure you can claim them. There may be other tax benefits you can get when you claim a dependent.
Related Information:
Your parents don’t have to live with you for more than half the year to qualify as a dependent. As long as you pay more than half of the household expenses for your parents, you can claim them as dependents even if they live elsewhere.
For more information check Here.