Continental Illinois Corp. shareholders, who lost most of their stake in the bank company when the government rescued the failing institution last summer, probably will lose the rest, the company told them yesterday.

Last summer, as part of the Federal Deposit Insurance Corp. bailout of Continental, stockholders took a $1 billion loss, reducing their interest in Continental to $800 million.

The FDIC got rights to new stock representing about 80 percent of the outstanding shares of Continental and put a lien on the old shareholders' equity to cover losses the regulatory agency might suffer as a result of the rescue.

The FDIC bought loans with a face value of $3.5 billion for $2 billion and agreed to buy another $1.5 billion in bad loans if the big Chicago bank wanted to unload them.

Investors shares in Continental Illinois Corp., whose principal subsidiary was the weakened bank, were transferred to a new company, Continental Illinois Holding Corp., and they received one share of the holding company for each share of Continental Illinois Corp. they owned.

Continental Illinois Holding Corp. said yesterday it appears that by Sept. 26, 1989, the FDIC will lose an additional $800 million on the loans it bought from Continental and will exercise its right to the remaining $800 million in equity Continental shareholders have left.

Even if shareholders had some equity remaining after losses on the first $2 billion of FDIC investment, the losses on the additional $1.5 billion the bank said it expects to sell the FDIC would likely wipe out shareholders, the report said.

The bank already has sold $272 million of the $1.5 billion to the government.

The restructured Continental, meanwhile, has rebounded sharply after shedding many of its problem loans. FDIC Chairman William M. Isaac said recently that the agency probably will begin selling some of its 80 percent stake in the rescued Continental within two years -- far earlier than the agency expected.