The Bonus Bond scheme has now entered into wind-up mode and bondholders can no longer cash in their investments.
Around $2 billion has already been redeemed by around 170,000 customers from the scheme.
It had $3.3b invested with around 1.2 million bondholders when ANZ announced on August 25 that it would stop taking new investments and look at winding up the scheme due to low interest rates reducing the prize pool.
ANZ Investment Services, which manages the scheme, said today the wind-up began at 9pm on Saturday.
During the wind-up, the supervisor and the manager will calculate and distribute the remaining funds to investors.
Final distributions from the wind-up cannot be paid until term deposits that the scheme invests in have matured or been otherwise realised, the final winding-up expenses have been confirmed and the ANZ has bank account details from Bondholders to make payments.
Ben Kelleher, managing director retail and business banking for ANZ, said it was confident remaining bondholders would receive a share of reserves over and above their original investment.
"While the process to confirm the final amount that each bondholder is entitled to is complicated and may take twelve months or more, we expect to distribute a large portion of what each bondholder is entitled to sooner than this.
"If this happens bondholders will receive their total distributions in more than one payment."
Redemption requests received before 9pm on October 31 would continue to be processed and paid.
Bonus Bonds were launched by the New Zealand Government through the Post Office in 1970 and the scheme was then bought by the ANZ bank.
Instead of getting interest on their investments savers went into a monthly draw to win a prize of up to $1 million but the odds of winning a prize were low and had been getting worse.
Last year's annual report said the average odds were one in 32,294 of winning a prize in any given month, down from one in 26,875 in its 2018 financial year.
It has also come under fire in recent years for its high levels of fees compared to payouts for investors.