Absent parent – this term applies to the area of Family Law in some legal systems. There it refers to the figure of a parent who is obliged (usually via court decision) to pay monthly financial support towards their child. This child dough lives with the other parent and this is the legal reason for getting support.
The term could also have another meaning – of a parent who has abandoned their own child. So the social service Authority usually takes care of the child and finds a foster parent for it.