No, according New York CPLR § 5209, entitled, "Discharge of garnishee's obligation."
Assuming the Income Execution itself contains the basic information required in CPLR § 5231, the injured employee-debtor may not seek damages against its employer. An applicable scenario would be when somebody is accidentally targeted for someone else's debt, and the employer honors the income execution without investigating the merits of the case or its procedural appropriateness (jurisdiction, for example).
An income execution is used interchangeably with wage garnishment. It's the process whereby a marshal or sheriff seizes part of your wages to satisfy a judgment. A garnishee refers to any party who holds money or property belonging to the judgment debtor (employee). Employers paying out wages are garnishees.
This statute was affirmed in Chin Sung Yu v Riggs Nat. Bank of Washington, D.C. The 1998 appeals court held that "garnishee's compliance with CPLR 5209 is a safe harbor that preempts the judgment debtor's common-law claim that the garnishee should have investigated the validity of the execution." Turn to the creditor, not the employer, suggested the court.
The statutorily prescribed "Notice to Judgment Debtor or Obligor" and the 20-day Marshal/Sheriff notice required under CPLR § 5231e are supposed to afford the debtor notice protection to satisfy due process. But if the judgment creditor prosecutes the entire action using an outdated address, these notices are rendered meaningless.
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 248 AD2d 235 (1st Dept 1998).