All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If your father had died while having a delayed dowry to pay to your mother and your mother did not renounce it for him, then she is still entitled to ask for it. It should be paid from his inheritance before its distribution among his heirs. If the inheritance had been distributed among them, then it should be recovered from every inheritor according to his/her share to cover her dowry or that the heirs should take the responsibility of paying it themselves.
This is, of course, if your father had left money behind him. However, if he died while not leaving any money behind him, then the heirs are not obliged to pay it for him.
In fact, if you or someone else pays it on his behalf, then this is a form of righteousness to your father and he becomes then free from his obligation –Allah willing.
Allah knows best.