Well, let’s see…wouldn’t that be a pronoun that serves as an adjective?

Like:

“The boy was doing HIS homework.” (i.e., the homework that he was assigned, not homework from someone else’s class).

“The girl was tying HER shoe.” (i.e., the shoe she is wearing, not her little brother’s shoe).

Pronominal adjectives, words primarily pronouns, but used adjectively sometimes in modifying nouns instead of standing for them. They are of two kinds,—RELATIVE and INTERROGATIVE,—and are used to join sentences or to ask questions, just as the corresponding pronouns do. 149. The RELATIVE ADJECTIVES are which and what; for example,— It matters not what rank he has, what revenues or garnitures. —Carlyle. The silver and laughing Xenil, careless what lord should possess the banks that bloomed by its everlasting course. —Bulwer. The taking of which bark. I verily believe, was the ruin of every mother’s son of us. —Kingsley. In which evil strait Mr. Oxenham fought desperately. — Id. 151. The INTERROGATIVE ADJECTIVES are which and what. They may be used in direct and indirect questions. As in the pronouns, which is selective among what is known; what inquires about things or persons not known. Sentences with which and what in direct questions:— Which debt must I pay first, the debt to the rich, or the debt to the poor? —Emerson. But when the Trojan war comes, which side will you take? —Thackeray. But what books in the circulating library circulate? —Lowell. What beckoning ghost along the moonlight shade Invites my steps, and points to yonder glade? —Pope. In indirect questions. Sentences with which and what in indirect questions:— His head.. . looked like a weathercock perched upon his spindle neck to tell which way the wind blew. —Irving. A lady once remarked, he [Coleridge] could never fix which side of the garden walk would suit him best. —Carlyle. He was turned before long into all the universe, where it was uncertain what game you would catch, or whether any. — Id. At what rate these materials would be distributed and precipitated in regular strata, it is impossible to determine. —Agassiz.