If I claimed a dependent who lives with me can they still file a tax return

You do not report his/her income on your return. If it has to be reported, at all, it goes on his own return.  Your dependent  must file a tax return for 2021 if he had any of the following:

1.          Total income (wages, salaries, taxable scholarship etc.) of more than $12,550 (2021).
2.          Unearned income (interest, dividends, capital gains, unemployment, taxable portion of 529 distribution) of more than $1100.
3.          Unearned income over $350 and gross income of more than $1100
4.          Household employee income (e.g. baby sitting, lawn mowing) over $2300 ($12,550 if under age 18)
5.          Other self employment income over $432, including money on a form 1099-NEC

Even if he had less, he is allowed to file if he needs to get back income tax withholding. He cannot get back social security or Medicare tax withholding.

In TurboTax (TT), he indicates that somebody else can claim him as a dependent, at the personal information section. TT will check the "can be claimed as a dependent" box on form 1040.