Does the sole son inherit the entirety of his deceased father's estate, in the event that the deceased had a missing full brother upon whom there were expiations for debt?

The first thing to be done with a deceased's estate, after the expenses of preparing the body for burial, is to pay off their debts, according to the Prophet's (peace be upon him) saying: "The soul of a believer is attached to his debt until it is paid off." This includes expiations (kaffarat).

Whatever remains of the estate after settling the debts is for the son by way of 'asaba (agnatic inheritance), and there is nothing for the missing full brother because he is completely excluded (mahjoob hirman) by the son.