In a Chapter 13 bankruptcy repayment "plan", can the debtor offer a payoff LESS than the actual amount owed?

Normally with a chapter 13 (depending on your income) unsecured debts are discharged. In some cases with secured debts you can pay less than you owe, i.e. you are including a vehicle in the trustee payment, if it is worth less than you owe it can sometime be renegotiated through the bankruptcy process. This does not seem to be the case with houses though.