Do you recover via a debit to the account? If so any OP outstanding at point of death would be the responsibilty of the executors and this may be the surviving partner.
This would be the position re outstanding arrears on the account as liability would end then (unless it is a joint and several liability and the deceased is not the primary responsible person).
An OP on death , if the primary liable person were the deceased, would be offset against the reduction in liability and so would not, in reality, be payable by the executors. I therefore have assumed, in this reply, that the OP to which you refer was a previously calculated OP that they deceased was paying via CT instalments and there were arrears on the account.
Do I know what I'm doing? The jury's out on that........................