After any partial payment authorized pursuant to this section has been paid, interest and penalties shall be charged against the unpaid balance only. The acceptance of a partial payment by any official pursuant to this section shall not be deemed to affect any liens and powers of any municipal corporation conferred in any general or special act, but such rights and powers shall remain in full force and effect to enforce collection of the unpaid balance of such tax or tax liens together with interest, penalties and other lawful charges.
N.Y. Real Prop. Tax. Law § 928-A