Is it permissible for the deceased's children and wife to ask their grandfather to waive his share of the inheritance before the estate is inventoried, in exchange for committing to financially support him, in order to avoid the complexities of inheritance in the event of his death, and would they incur sin for doing so?

It is not permissible to waive the grandfather's share of the inheritance for financial compensation, because it is a reconciliation over an unknown quantity. Selling an unknown quantity may not be permissible, and some imams do not validate it; Imam Al-Shafi'i held this view. Furthermore, reconciliation over an unknown quantity is valid if there is no way to ascertain it, but what can be known, reconciliation over it is not valid while it remains unknown.

However, if the grandfather is sound of mind and body, there is no harm in him waiving all or part of his right to the inheritance, provided that it is with his consent and without any request from the heirs. You must strive for justice and avoid consuming people's rights.