Amid the thousands of people caught up in the apparent multibillion-dollar fraud of Bernard L. Madoff, some investors stand out.

They made money.

One client said he invested more than $1 million with Mr. Madoff over a decade ago. As his portfolio rose in value, he took out several million dollars. While his statements showed several million dollars in his Madoff account when the fund collapsed last week, the client still ended up ahead.

How many clients of Bernard L. Madoff Investment Securities profited unwittingly on what Mr. Madoff described as a big Ponzi scheme isn’t known. But given the structure of Ponzi schemes, which use money from later investors to pay early investors, many longtime clients may actually have wound up ahead.

“In a Ponzi scheme, not all investors lose,” said Tamar Frankel, a law professor at Boston University who has written on Ponzi schemes. “Those who manage to get out in time retain their investments and some of their gains.”