Is the one who slaughters [the animal] burdened by the sin of his mother's negligence in caring for the poultry she raises, and what should he do about it?

Feeding and watering confined animals is obligatory upon their captor, to the extent that satiates them and quenches their thirst. The captor is required to undertake this, spend on them, and appoint someone to care for them, because failing to do so constitutes torture. The owner of a permissible dog must feed and water it or release it. It is not permissible to confine any animal to perish from hunger or thirst. If the captor refuses to feed them, he is compelled to sell them, feed them, or slaughter those that are permissible for slaughter. If he does not comply, the ruler acts on his behalf.

Therefore, feeding is obligatory upon your mother, not upon you. You should advise your mother kindly and remind her of the seriousness of confining animals and neglecting to feed them, and the severe warnings that have been mentioned regarding this.