There are 1.3 million people who own Bonus Bonds but questions have been raised in the past about how many of those are dead or haven't claimed prizes because they have shifted house and not updated their contact details with the bank.
An ANZ spokeswoman confirmed about 2000 customers were currently recorded as deceased on its Bonus Bonds register.
"Generally these accounts are in the process of being closed with the estate or it's a joint ownership where one of the customers is still alive."
She said on average the bank received and processed 740 notices of deceased estates each month.
"When we are notified of a customer passing away, we work with the estate to release the funds. The timing depends on how quickly we can receive the necessary documentation from the estate."
But unclaimed prizes just get turned into more Bonus Bonds.
The ANZ spokeswoman said it contacted all winners with a phone call, letter or online notification depending on the value of the prize and the bondholder's prize payment instructions.
"When a payment to a bank account is returned or when we've sent a prize winner a cheque and it hasn't been banked within six months, we will issue the winner Bonus Bonds instead of paying a cash prize.
"This is outlined in our Bonus Bonds Product Disclosure Statement. Where a customer's current address is not known or they have not met identification requirements we will issue the winner Bonus Bonds rather than paying the prize in cash."
The comments come as Bonus Bonds are in the sights of the Financial Markets Authority as it looks at legacy products that may no longer be suitable for investors.
The financial watchdog says it found issues with legacy products as part of its conduct and culture review of the banks and will be looking further at the issue as part of the new conduct licensing regime announced by the Government last week.
The FMA's response came after the Herald queried the regulator over complaints and concerns about Bonus Bonus after revealing an ANZ staffer had written to the bank's chief executive and board concerned about the product and calling it the "biggest rort in financial services in New Zealand" and asking for the fees to be cut.
A spokesman for the FMA said it had received four anonymous complaints in the last five years regarding ANZ's Bonus Bonds.