If you are providing over half your mother's support and her only income is Social Security, then you will be able to claim her as a qualifying relative.  You get a $500 credit for other dependents on your own tax return for claiming her.  You do not receive stimulus money for claiming her, nor will she receive a stimulus check if she is claimed as someone else's dependent.

CREDIT FOR OTHER DEPENDENTS

https://ttlc.intuit.com/questions/4499708-what-is-the-500-credit-for-other-dependents-family-tax-cre...

The income limit does not include social security benefits. However, if her benefits result in your providing less than half of her total support, that would prevent you from claiming her as a dependent. Here are the requirements to claim a qualifying relative dependent:

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross taxable income for the year must be less than $4,200 in 2019. This excludes social security benefits. 
4. You must provide more than half of the person's total support for the year. You must include social security benefits in determining this. 
5. The person must be a U.S. citizen, U.S. resident alien, U.S. national, or a resident of Canada or Mexico.

Nontaxable Social security doesn't count as income, for the $4200 income test, but social security money she spends on her self does count as support not provided by you, for the support test. Money she puts into savings & investment does not count as support she spent on herself.

Note that a parent is closely related so there is no requirement that she live with you at any time, during the year. But if you provided a home it helps your support case, unless she owns the home you live in. If no one person (or married couple) provides 50% of the support (for example your siblings are also sending support), then a "multiple support agreement” (IRS Form 2120) can be used, to allow you to claim the dependent. https://www.irs.gov/pub/irs-pdf/f2120.pdf

The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf The support value of a home is the fair market rental value, divided by the number of occupants.