my mom is trying to apply for residency through my sister who is a us citizen. My mother is 64 and has been living in the us since 1991.

Your sister will need to file an immigrant visa petition on behalf of your mother. Your mother may be able to request adjustment of status to a permanent resident. This would allow her to become a resident without leaving the country. It is not clear whether your mother is eligible for adjustment of status. To be eligible, your mother would have had to have been admitted or paroled into the country. She also cannot be subject to a deportation order. You can read more about family immigration at http://myattorneyusa.com/family-immigration.