Normally, a singular antecedent requires a singular pronoun. But, because he is no longer universally accepted as a generic pronoun, referring to a person of unspecified gender, people commonly (in speech and in informal writing) substitute the third-person-plural pronouns they, them, their, and themselves (or the nonstandard singular themself), Chicago Manual of Style, 17th edition, p. 241.
So, I like that themself is acceptable as a singular pronoun in general writing, as in the following:
At least take your phone with you. A person should be careful when walking alone; they could find themself facing great danger.
Although themselves may be used as a singular gender-neutral pronoun, it just does not have any of the trappings of a singular word—referring to just one person. Themself is not such an alien word. It enjoyed popular usage in centuries past. I agree with the adage that what falls out of favor in one century can crawl back into acceptable usage later on. There is nothing new under the sun. Now we accept they as a singular gender-neutral pronoun; so, now it’s time to welcome themself to the table.
There are other candidates for singular gender-neutral pronouns floating around out there, for example, the strange-sounding xeself. However, they are not yet popular and none have stuck the landing, so to speak. Here are five of them, taken from the Free Dictionary.
Once you know your audience and feel confident about the best way to get their attention, the golden rule is to be consistent in your usage of that word you choose throughout your document or manuscript.
More on this at https://stancarey.wordpress.com/2014/01/23/the-unsung-value-of-singular-themself/
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The Dutty 