I learned three cases where "their + singular noun" is preferred.
1, The noun is an shared object.
The couple love their life together. (their shared life)
2, It is perhaps somewhat more common when speaking of "people in general" or any large and poorly defined group, to use a singular form, as if speaking of each individual member of the group member. But sometimes this doesn't seem to work well. Or a writer chooses the plural form as a matter of style. Or uses "a person" instead of "people", speaking of a typical example, and using singular forms.
Nowadays, a growing number of people with health problems are trying alternative medicines and treatments instead of visiting their usual doctor.
Nowadays, people are spending more time away from their home because they spend longer in their workplace.
Most employees prefer to eat lunch at their desk[s]. (desk or desks depends on personal preferences)
Still, when I come across a long text, I have trouble using what I learned to analyze.
When deciding between postgraduate studies and work, students should consider a variety of factors, including their career plans, financial status and personal preferences.
The first factor that undergraduate students should consider is their intended career.
The second factor that students should take into consideration is their financial situation.
The final factor that undergraduate students should consider is their own personal preferences. Some students may have entrepreneurial ambitions and dream of running their own business.
By taking career goals, financial status and personal preferences into consideration, students can improve their chances of making an optimal choice.
I think throughout the essay "they" speaks of a single student. "Status" is usually an uncountable noun, so I have no problem with that. But for the rest nouns, why some are plural, some singular? Is the author's every choice well-considered?