In the world of unusual insurance coverage, some of the wildest risks are those where protection is requested, even offered, but never sold. Think of them as the weird risks that got away.

Jonathan Thomas, divisional underwriter for accident and health at Canopius Managing Agency, operating in the Lloyd's market, recalls the policy requested by an unnamed actor seeking protection against loss of chest hair.

The firm developed a policy that would kick in after more than 85 percent of the hair was lost. In order to collect on the policy, a panel of trichologists would have to make a finding of hairlessness. Lloyd's came up with a price, but the insurance was never purchased, Mr. Thomas noted.

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