Actually, the sentence is perfect. Probably, it might be a mistake at the exam.
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Adverbs, dear friend, adverbs.
For example, think "time".
My mother likes being responsible lately for people's lives.
My mother likes being responsible daily for people's lives.
My mother likes being responsible recently for people's lives.
Or, as in my case...
My mother likes being responsible unapologetically for people's lives.
As a student of English language for quite sometime now, I think the space needs to be filled out with any suitable noun such as "person" "individual" "citizen" etc. Any other suggestions please ?