As of 2016, Americans can receive Supplemental Nutritional Assistance Program, or SNAP, benefits while receiving Social Security benefits in every state except California. "Food stamps" is the former name for SNAP, a program that currently uses electronic cards rather than paper stamp books.
Receiving Social Security benefits only affects SNAP in California, because the state provides its own food benefits to people receiving Social Security. The food benefits provided by the state are so large, California residents would only be eligible for the $10 minimum benefit from SNAP, a federal program. Rather than process paperwork for such a small sum, California adds on an extra $10 to the Social Security benefits it provides to seniors and the disabled.
In other states, Social Security benefits are ignored when calculating a person's eligibility for SNAP. The program also has a higher countable resource limit if the person applying is a senior or disabled. Countable resources include possessions and income.