Two branches of civil law matter here. Contract law enforces duties the parties agreed to take on, such as an insurance policy. Tort law covers civil wrongs, such as negligence, that breach a duty the law imposes whether or not any agreement exists. Neither one is a crime by definition, and an insurance policy is governed by contract law.
A contract is enforceable only when four elements are present. Mnemonic: OCCL.
Offer and acceptance: in A&H insurance, the applicant usually makes the offer by submitting a signed application with the initial premium; the insurer accepts by issuing the policy as applied for. If the insurer changes the terms, such as charging a higher premium, that is a counteroffer the applicant can accept or reject.
Consideration: the value each side gives. The applicant gives the premium and the statements in the application; the insurer gives its promise to pay covered losses. Consideration does not have to be equal.
Competent parties: each party must have the legal capacity to contract, meaning of legal age and sound mind. A person a court has declared mentally incompetent, or someone who is intoxicated, cannot form a valid contract. An older or chronically ill applicant is still competent: age and health affect underwriting, not capacity. Corporations and noncitizens can contract too.
Legal purpose: the contract must have a lawful object. An agreement to do something illegal is unenforceable, however clearly the parties agreed and whatever they paid.