'Never' is an adverb which means 'at no time', 'on no occasion' 'in no way', 'not at all'. 'Never' does not affect the form of the verb which depends on the subject. In your example the subject is 'She' so the correct verb form is 'stops'. Never is placed infront of the main verb in a sentence for all verbs except 'to be', when it comes after the main verb. 'I never study.' I will never go to visit her.' 'I am never tired'. Never is negative in concept and is therefore always used with a positive verb. You cannot say 'I don't never eat meat' as happens in some other languages because this then becomes a double negative.

"Never" is also the same as "do/does not ever" She never stops thinking. = She does not ever stop thinking.