NEW YORK — The many Bernard Madoff investors who withdrew money from their accounts over the years are now wrestling with an ethical and legal quandary.

What they thought were profits was likely money stolen from other clients in what prosecutors are calling the largest Ponzi scheme in history. Now, they are confronting the possibility they may have to pay some of it back.

The issue came to the forefront this week as former Madoff clients began to receive letters inviting them to apply for up to $500,000 in aid from the Securities Investor Protection Corp.

Lawyers for investors have been warning clients to do some tough math before they apply for any funds set aside for the victims, and figure out whether they were a winner or loser in the scheme.

Hundreds, maybe thousands of investors in Madoff's funds have been withdrawing money from their accounts for many years. In many cases, those investors have withdrawn far more than their principal investment.

No one knows yet how many people will emerge as net winners in the scandal, but the numbers appear to be substantial. Many of Madoff's long-term investors have, over time, cashed out millions of dollars of their supposed profits, which routinely amounted to 11 percent to 15 percent per year.

Jonathan Levitt, a New Jersey attorney who represents several former Madoff clients, said more than half of the victims who called his office looking for help have turned out to be people whose long-term profits exceeded their principal investment.

"There are a lot of net winners," he said.

Asked for an example, Levitt said one caller, whom he declined to name, invested $1.8 million with Madoff more than a decade ago, then cashed out nearly $3 million worth of "profits" as the years went by.

On paper, he still had $4 million invested with Madoff when the scheme collapsed, but it now looks as if that figure was almost entirely composed of fictitious profits on investments that were never made, leaving his claim to be owed anything unclear.

Other attorneys report getting similar calls.

Under federal law, the court-appointed trustee trying to unravel Madoff's business can demand that people who profited from the scheme return some or all of the money.

These so-called "clawbacks" are generally limited to payouts over the past six years, but could still amount to big bucks for some investors.

When a hedge fund run by the Bayou Group collapsed and was revealed to be a Ponzi scheme in 2005, the trustee handling the case sought court orders forcing investors to return false profits. Many experts anticipate a similar process in the Madoff case.

Applying for the aid could give the trustee evidence he needs to initiate a clawback claim. On the other hand, investors who ignore the letter would most likely forfeit any chance of recovering lost funds.

No matter how they respond, it may only be a matter of time before investors wiped out in the scandal turn on those who unknowingly enjoyed the fruits of the fraud.

The future is equally cloudy for investors who cashed out entirely before Madoff's arrest.

Their lucky ranks include the Fort Worth Employees Retirement Fund, which invested $7.5 million in a Madoff-related hedge fund years ago, then cashed out last summer after a consultant raised concerns about the investment.

Fort Worth walked away with $10 million — a sum that included $2.5 million in what now appears to be fraudulent profit.

A lawyer for the public pension fund, Robert Klausner, said he couldn't discuss whether that money might have to be returned, but said the decision to divest was not made because of "special or inside knowledge of what was later reported to be misconduct."

"There just aren't any winners in this deal," Klausner said.

Stephen Harbeck, chief executive of the Securities Investor Protection Corp., told The Associated Press neither he nor the trustee handling Madoff's business, Irving Picard, have decided what to do about Madoff investors who made money. He predicted the process would be "a legal and accounting nightmare."

"Between money in and money out, versus statements received, it is a real difficult pile of issues," Harbeck said. "There are some customers who would want us to use clawback procedures against other customers, and there are other customers who would resist that."