It's common to use 'their' with singular in English to allow for both genders.
Singular they - Wikipedia, the free encyclopedia
Student or Learner
In the following passage:
'No veteran who has served and risked their life ... should have to worry about their personal safety.....'
'Veteran' is singular, so why does the author use 'their' instead of 'his'?
(1) When I was younger, English speakers would use his in your
sentence because for a long time his referred to both genders.
(2) Then in the 1960's, many groups in the United States expressed
dissatisfaction with their treatment.
(a) Many women resented the pronouns he, his, him being used to
refer to women.
(i) As a result, many people now have decided to use their as a pronoun
to please both genders.
(a) If you are not comfortable with their (I personally am not), you
his or her
she or he (instead of they)
Whenever possible, some people write a sentence so that it is not
necessary to use a personal pronoun or they make the noun plural
in order to match their.
The use of their is very widespread in British English and I use it and the only people who have complained about our using it on the site have been AmE speakers. I think that BrE is generally more relaxed about singular and plural issues.
Yes, I have studied that plural "they or their" is used in singular in order to avoid gender distinction like in "Someone's forgotten their bag"