In some families, if the child is already earning a salary that is enough to cover family expenses, he or she doesn't have to wait for the parent to request money before they can start assisting the family. Some will even ask the parent to stop paying rent and use the money for other things. It's just a matter of self-decision. If you are to talk about legality, the girl is off-aga and is entitled to pay her own bills where necessary.
Exactly my thought as well. Moreover, it's not a matter of some family, it is what every responsible child should be doing as far as they have start earning a reasonable amount. Although, things like this depends on the condition of one's family. Some families who are doing good might not pay attention to issues like this but families surviving with a limited resource will definitely consider the child paying some part of the bill. Regardless, as a working class child earning decent amount, it's expected to be a helping hand to one's family.
As the way Op put it, it's not ideal for parents to demand rent from their child if they stay together unless the child is willing to pay. In as much as responsible child will do what is necessary of him, it is the responsibility of the parent to cater for the children irrespective of their class until they can not longer do so at their old age and then reverse will be the case.