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There has been a tendency in English toward using singular "they" in the non-specific case, like "someone knocked on my door and they left a package".  This is more common in speech than in writing, but becoming more common in both.  People will usually understand what you meant.  Some people will experience cognitive dissonance from the number mismatch (especially in vaguer cases where you could have been referring to either one person or more than one).

You *can* do it -- demonstrably: people do.  As a writer I feel it is better to avoid this usage because it causes confusion and is almost never necessary.  You can just as easily write "someone knocked on my door and left a package" -- no pronoun needed.  If you're documenting a process and need to write something like "a user edits (their) profile by...", you can instead take other approaches:

- Switch to plural: "users edit their profiles by..."
- If it's documentation *for* the user, use second person (everywhere, not just in sentences like this): "to edit your profile, ..."
- Replace the pronoun: "a user edits a profile by..."

You almost never *need* to use non-specific singular "they" in writing.  There are other ways to convey the information clearly.  In speech, which is by its nature more immediate, you'll probably both say and hear it.

All of that is for the *unspecified* case -- you're talking about an individual, but you don't know who -- a generic person.  In recent years some people have started using "they" as a personal, *specific* pronoun -- people who are nonbinary or otherwise do not identify as "male" or "female".  This is an evolving area of language.  I think this is not what you meant to ask about, so I'm not trying to address it here other than to note that it is a different case than the non-specific usage of singular "they" for which remedies exist.