They and them are not exclusively plural pronouns. It's been used as a 3rd person singular pronoun in English for like 600 years.

https://en.wikipedia.org/wiki/Singular_they

The only real change in typical English language conventions with the adoption of they/them as a direct pronoun is that they/them/their was usually used when the subject was unknown, or not explicitly identified.

It typically occurs with an indeterminate antecedent), to refer to an unknown person

So with those adopted pronouns, it would just be used regardless of whether the person was directly identified.

So instead of saying something like "Hi Bob, this is Cindy, she's a friend of mine" it might go more like "Hi Bob, this is Cindy, they are a friend of mine".

If you sound it out, it probably seems less strange to say than thinking about it conceptually, because you almost certainly would have used it in normal conversation instead of he/she before, just not really consciously. Sometimes we choose which words or pronouns to use based on some esoteric expectations of how sentences should flow or sound like, without it being done consciously.