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NEW YORK — Knight Capital Group survived a near-death experience on Monday, lining up Wall Street firms to lend it badly needed cash after the brokerage lost $440 million last week when a malfunction in its trading system flooded the market with erroneous trades.

But the rescue, which came down to the wire, had a steep price: control of the firm. And it is still not certain that Knight will make it through the episode intact.

Knight’s new investors will gain a 73 percent stake in the company and three board seats. The value of current shareholders’ stake will also be heavily diluted. And Knight, which has removed the problem software and is still completing its own investigation of what went wrong, faces a difficult task of rebuilding trust with clients and persuading regulators that Wednesday’s problem was an anomaly. Its stock has plunged 70 percent since last Tuesday, before the glitch happened.

‘‘This is an isolated situation,’’ Knight’s chief executive, Thomas Joyce, said on CNBC Monday morning. ‘‘We screwed up. We paid the price.’’

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All weekend, speculators wondered whether Knight would be able to open for business Monday. The technical glitch briefly sent dozens of shares swinging wildly last week, and the company had to drain its capital to atone for the sin by covering the erroneous trades.

The trading disaster Knight caused has revived a thorny debate about the merits of high-speed trading, where lightning-fast mathematical algorithms trade stocks in milliseconds and, as recent mistakes indicate, strain the system that is supposed to handle them.

More and more stock trading is handled by computers, and many market players have called for stricter controls to prevent disasters from happening. The mistakes have eroded shareholders’ confidence that they can trust the system — a point punctuated again Monday, when a technical problem shut down markets in Madrid for five hours.

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Early Monday morning, before the stock market opened at 9:30 a.m., it still was not clear whether Knight was OK.

Just after 7 a.m., Knight made a regulatory filing saying it had secured a $400 million lifeline but that the deal wasn’t yet sealed.

An hour later, the New York Stock Exchange threw another twist into the story, announcing it had temporarily reassigned some of Knight’s trading responsibilities to a rival firm.

At 9:22 a.m., Knight announced that the deal was completed, but didn’t say who the investors were. At 9:24 a.m., it did.

Once trading opened, Knight’s stock moved sharply lower in heavy trading. It ended the day down 98 cents, or 24 percent, at $3.07. That was far below its closing price of $10.33 on Tuesday, the day before the debacle occurred.

Knight Capital is a trading firm that takes orders from big brokers like TD Ameritrade and E-Trade. It then routes them to the exchanges where stocks are traded, like the New York Stock Exchange.

One of the roles Knight plays in the stock market is that of a ‘‘designated market maker.’’ Those firms are responsible for keeping trading of the stocks they oversee orderly.