Illinois insurance regulators prohibited the company from making interest payments in June and July on the bonds, Lumbermens spokeswoman Linda Kingman said.
Analysts said the default stems from a failed expansion effort, in which the insurer charged too little for policies and spread itself too thin.
The buyback offer is valid through May 1, the company said.
Kemper announced this month it would stop underwriting policies and sell its main businesses to Swiss Re's Securitas Capital LLC and other private-equity funds.
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