Lisnaholic

Yep, especially in conversation, we use They/Them/Their even when we are refering to only one person. Here's a couple more examples of how we do it:-

"Someone left their cellphone on the table." It's clearly one person but we never say "his or her cellphone" and we even more neverly say "its cellphone."

Person A: "Hey, there's a person at the door who wants to speak to you!"
Person B: "Whoever it is, can you tell them to wait. I'm just finishing a post on MB."
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Another option, which is becoming less and less politically correct, is to just assume that it's a man:-

"I don't know who designed this building, but he did a good job."
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Some of the examples posted seem to be mixing up another use of "They", which is when, grammatically, we need a subject for a verb, but we don't know or don't really care who the subject is. We say it without even thinking about whether it's a single or plural subject, e.g:-

"Hey! They've mended the hole in the road!" (If we think about it, probably plural.)
"I went to the shop and they gave me the wrong change." (If we think about it, probably single.)

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"Am I enjoying this moment? I know of it and perhaps that is enough." - Sybille Bedford, 1953