Singular “their”.

“The people forgot to feed their cat”.

That’s a normal use for the word “their”. “Their cat sleeps a lot”. They have a cat. They cat sleeps.

Sometimes we use their to refer to a singular. For example:

“Somebody forgot their phone at my house”. We do that because we don’t know who left the phone. If there were only men or only women, you could say “his” or “her”.

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