New York General Obligations Law Section 15-701 - Surety not discharged by failure or refusal by creditor to sue principal debtor.

 15-701. Surety  not  discharged by failure or refusal by creditor to
  sue principal debtor. Unless otherwise agreed  between  the  parties  in
  writing,  the  failure  or  refusal  by  a creditor, after a demand by a
  person bound as surety, to bring an action against  a  principal  debtor
  upon  a  contract  hereafter made or an obligation hereafter created for
  the payment of money or the performance of any act shall  not  discharge
  such surety.

Last modified: February 3, 2019