The fuller, New York statutory definition is this: "the whole residue, or so much thereof as the court may determine to be just and equitable, of the debt remaining unsatisfied, after a sale of the mortgaged property and the application of the proceeds, pursuant to the directions contained in such judgment, the amount thereof to be determined by the court as herein provided.
The plaintiff's attorney (in other words, the bank's lawyer) must make a motion to receive such a deficiency judgment. Otherwise, the amount gained from the sale shall be deemed the full amount owed, and the plaintiff has no right to collect the additional debt. However, if the parties (mortgagor and mortgagee) have already agreed in their mortgage or promissory note, then the debtor could be liable for the full amount.
A debtor who has a deficiency judgment should see an attorney for possible remedies, including bankruptcy, an exemption from creditors, an appeal, or a motion. As with all legal research sources on-line, Internet users should take caution before applying such advice to your own case, and perhaps should consult an attorney, barrister, or solicitor.