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Wiktionary
underinsured

a. 1 not having sufficient insurance to cover loss or damage 2 (context US English) not having proper health insurance n. One who has insufficient insurance.

Wikipedia
Underinsured

Underinsured refers to various degrees of being insured for some real risks and uninsured for others, at the same time.

Usage examples of "underinsured".

For such a conscientious man, I am surprised that my father underinsured the house contents.