An unrelated deadbeat (or otherwise down on their luck) roommate who lived with the taxpayer all year can sometimes qualify as the taxpayer's "Qualifying Relative" (QR) dependent. (Check the rules in Table 2 here to be sure.) In that case, the taxpayer would be entitled to claim a dependent exemption for the deadbeat roommate and subtract the value of his $3,700 exemption from his taxable income.
However, unrelated roommates--even if they are QR dependents--are NEVER "Qualifying Persons" (QP) for the Head of Household (HoH) filing status!
HoH filing status requires that the taxpayer support a household containing a sufficiently related "QP". Unrelated roommates, girlfriends, boyfriends, or even distant relatives such as cousins are NOT QP's for HoH status, even though they might be QR's for dependent exemption purposes.
How "closely related" does a QP have to be for HoH status? Check the table on page B-3 here.
Once again, this illustrates that the IRS does not use English the same way the rest of us do. You don't necessarily have to be "related" by blood or marriage to be a "Qualifying Relative" dependent, but you DO have to be closely related by blood or marriage to be a "Qualifying Person" for HoH status.