You can generally claim your disabled boyfriend's mother on your taxes if she meets certain criteria. She must have lived with you for more than half the year, earned less than $4,700 in gross income, and you must provide more than 50% of her total support. If these conditions are met, she can qualify for the Credit for Other Dependents. She must be U.S. citizen, U.S. national, U.S. resident, or a resident of Canada or Mexico. Additionally, she cannot file a joint return with someone else unless it's only to claim a refund of withheld income tax or estimated tax paid.
For more information, you can refer to the IRS guidelines on claiming dependents and TurboTax's article on claiming a dependent.