grammar - Should a noun after the determiner *their* take in the form of singular or of plural?

Should I say

Some people use the word "flat" to describe their phone when its battery is dead.

or

Some people use the word "flat" to describe their phones when their batteries are dead. (I wanted to use "their" here to refer to the phone's instead of the people's)

or

Some people use the word "flat" to describe their phones when their battery is dead. (I wanted to use "their" here to refer to the phone's instead of the people's)

Which one is grammatically correct and why?

Answer

From the comments, it appears that you want to refer to 'some people' for which the pronoun is obviously their) and 'their phones', but use a singular battery. Put like that, it is clear that you will have to rephrase, since there is no correct pronoun for both singular battery and plural phones.
Your first example is common, but you should be aware that 'singular they', though commonly used, is also commonly criticised. (e.g. here and here).

Your second is grammatical, but if there is a difference between 'the batteries belonging to the phones' and 'the batteries belonging to the people' (do you really think so?), then it is ambiguous, and cannot be rescued without changing the sentence: when the battery is dead or ...to describe phones with dead batteries would be common rephrasings.

Your third is simply bad English (mixing singular and plural), unless, unusually, all the phones (or, of course, all the people) share one battery.