There is no obligation to accept the plan after you apply.
You can cancel at any time during the underwritng process. Even after you get the policy or certificate, you still have a few days to turn it down, called the "free look" period. You have the opportunity to refuse coverage after you examine in writing exactly what you bought.
In most cases, the insurance company does not deposit your check, charge your credit card, or debit your bank account, until the application is approved.
In cases where payment is processed when underwriting is in process, the entire premium is refunded if you are denied or if you cancel prior to approval or during the "free look" period.
Application fees are uncommon, but if there is one, it is usually non-refundable.
Health insurance is also a month to month situation in that you pay in advance and can cancel your coverage any time. However, as long as you pay premiums the insurance company can not single you out for cancellation.