In my experience, a mortgage holder can refuse the payment after the NOD has been filed if the amount being paid is not the full amount in arrears.  This amount is stated on the NOD filed and the property owner should have received a copy upon upon your mortgage company or loan servicing company filing the NOD with your counties recorders office.

In today's economy, if you wish to make a payment, contact your mortgage holder and attempt a "work-out" program.  In most cases the lien holder will want to work with you, however, they are under no obligation if the amount is not what is entirely owed by the responsible party.

For more information, visit The United States Treasury Department to view the rules for participating and obligations of the homeowners.

I think the terms of the mortgage dictate what they can accept or cannot accept.  Accepting less than what was demanded nullifies the demand.  So if payments to bring the account current is what was demanded, then that is what they can accept.  Usually, that will be 5 payments.

If the state law gives a redemption period after the foreclosure has been completed, only balance in full along with all costs can be accepted.  You would have to have some type of redeeming reason for the lender to accept anything else.  A re-write of the terms [a loan modification ] may be possible if the lender has reason to believe that there will not be a future default.

With property values declining, you can understand why a lender would not want to delay the inevitable.  Losing less money by acquiring the property sooner is sometimes the route the lender prefers to travel.

Sending in one payment does not cure a default if the loan is in arrears for more than one payment.