What is the ruling of Islamic law regarding the entitlement of the person to whom I lent a sum of money, in exchange for a piece of gold that I lost, to be compensated for its current value after many long years?

Calling the lending of money "borrowing" is incorrect; the proper term is "loan," and the gold piece is collateral for the loan. The collateral (pledge) is a trust (amanah) which the pledgee (mortgagee) does not guarantee unless there is transgression or negligence. The loss of the pledged gold piece due to negligence necessitates guarantee (compensation), unless it was due to a cause beyond the pledgee's control. The borrower should have been informed of the loss of the gold at that time, and if its value was equal to the debt, an offset (set-off) would have occurred. The pledgee is liable for the value of the gold on the day it was lost, as it has replaced the collateral. The value of the collateral, if it perishes, is considered on the day of possession according to the Hanafis, and on the day of damage according to the Malikis.