To be your dependent, your parent must have less than $4050 of taxable income, and you must provide more than half her total living expenses.
Social security is not taxable, but investment income, 401K withdrawals, pensions, etc. usually are. I can't think of any way that she would qualify for a refund and still be your dependent, unless she had pension income (less than $4050) but that pension had tax withheld. (If it did, she would get that withholding back.)
As mentioned, you need to check the box on her return for "I can be claimed as a dependent by another taxpayer."
