Is it permissible for the sister's children to refuse to accept the settlement of their deceased father's debt, which was owed to their sister, knowing that "the soul of a believer is held in suspense by his debt"? And how is this debt to be settled if the sister's children do not accept it?

If the deceased's sister's children are the sole heirs, and they are adult and of sound mind, then their exoneration of the deceased from debt is valid and clears the deceased's obligation. However, if there are other heirs, or if some of them are minors or of diminished capacity, their right is not forfeited. In this case, the right of those adult heirs of sound mind who waived it is forfeited, but the right of those who did not waive it, or who are minors/of diminished capacity, remains. The children of the deceased must pay their share to them if the deceased left enough to settle the debt. Otherwise, it is recommended for the deceased's children to pay it.