You can deduct medical expenses that you pay for yourself, your spouse, your dependents, and for someone who could be your dependent except for their income. This last rule mostly applies to a person who pays medical expenses for an adult child or their parents for whom they provide more than 50% of their support.
If you pay more than 50% of someone's total financial support (who is not your relative), AND that person lives in your home all the days of the year, AND that person has less than $4300 of their own taxable income, then you can list them on your tax return as an "other" dependent, which is a $500 tax credit. But it is not a deduction for their expenses.
Except for medical expenses or the "other dependent" rule, there is no other tax deduction for paying someone else's living expenses.
