What is the ruling on burying a mother who died of bone cancer without ghusl or shrouding, given the impossibility of doing so six days after her death?

It is not permissible to bury a Muslim deceased person without washing and shrouding, as these are two obligatory duties. If buried without washing, it is obligatory to exhume and wash the body, unless there is a fear of its decomposition or disintegration. This is the view of the majority of scholars, contrary to Abu Hanifa, who believes that exhumation is not permissible.

As for exhumation solely for the purpose of shrouding, the correct view among the jurists is that it is not permissible. This is because the purpose of shrouding is to cover the body, which has already been achieved by burial, in addition to the inviolability of exhumation.

In this case, since your mother was buried a long time ago, her grave should not be exhumed.