NEW YORK (CNN/Money) - Troubled cable television operator Adelphia Communications Corp. announced Thursday that the Rigas family, which founded the company, will relinquish its control of the nation's No. 6 cable operator and transfer more than $1 billion in assets back to the company.

But the company also warned investors that after consultations with the Securities and Exchange Commission, it would increase to about $2.5 billion the amount of indebtedness to be included in its consolidated financial statements as of Dec. 31, in order to reflect the full amount of borrowings and interest expense by entities affiliated with the Rigas family through that time, estimated at $1 billion.

The company also said that, as of April 30, the amount of borrowing done by the Rigas family's entities for which it was responsible had reached $3.1 billion.

Last week, Adelphia announced it had failed to make interest payments totaling about $38.3 million on outstanding debt securities and an approximately $6.5 million dividend payment on a series of preferred shares. The threat of delisting of its common stock by Nasdaq could force the company to repurchase $1.4 billion in convertible notes held by entities other than the Rigas family's holdings, which would cost more than that due to accrued and unpaid interest.

The Rigas family will transfer back to the company another $567.4 million in those notes as a result of Thursday's agreement with the family, but that transfer will satisfy the Rigas family's obligations under a $202 million stock purchase agreement, and will also shift to the company the primary liability for about $365 million under the co-borrowing agreements. In addition, cable properties owned by the Rigas family that the company chooses to have transferred to Adelphia will be transferred to the company at their appraised value.

Company founder John Rigas and his sons Timothy, Michael and James Rigas have given up their positions on the company's board, and Michael and James Rigas have resigned their executive vice president positions with the company. Last week, John Rigas gave up his positions as chairman, president and CEO of the company, while Timothy Rigas gave up his chief financial officer position.

"This is an appropriate and useful step on the part of the Rigas family toward restoring the company's credibility with shareholders, lenders and the marketplace as a whole," said a statement from interim CEO Erland Kailbourne.

Shares of Adelphia (ADLAE: down $3.16 to $2.53, Research, Estimates) lost more than 50 percent of their value Thursday afternoon when they resumed trading for the first time since trading was halted last week due to the threat of delisting of the company's stock.