It may depend on what "homeless" means. To claim an unrelated person, as a dependent, you must have lived together the entire year.
There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit and student status test, a relationship test and a residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. The Other dependent (qualifying relative) credit is worth (up to) $500 per dependent and is non-refundable. That is, it can only be used to reduce an actual tax liability.
A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:
- Closely Related OR live with the taxpayer ALL year
- His/her gross taxable income for the year must be less than $4700 (2023) $5050 for 2024.
- The taxpayer must have provided more than 1/2 his support
- He must be a US citizen or resident of the US, Canada or Mexico
- He must not file a joint return with his spouse or be claiming a dependent of his own
- He must not be the qualifying child of another taxpayer
You did not have to provide the shelter to claim the dependent, but the shelter provide by others counts as support not provided by you. The support value of a home, provided by others, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants
