Deprivation of mother's parental rights and alimony

I read the news about a girl whose mother was deprived of parental rights by the court, and this woman was also obliged to pay alimony, even if she does not actually care for the child and does not live with her. I'm curious: can this happen in my situation if one parent has not participated in raising the child for a long time and does not provide financial support, and how exactly can one initiate the procedure for deprivation of parental rights and collection of alimony in such a case?