When is an OK time for an employee to drop their medical insurance? Can an employer force an employee to keep their health insurance?
An employee can voluntarily cancel coverage at any time only if the company is not having employee premium contributions deducted pre-tax.

An employee can voluntarily cancel coverage at any time only if the company is not having employee premium contributions deducted pre-tax.
If they are, they are de facto enrolled in a Section 125 Plan and cannot change that election until Open Enrollment or a Qualifying Life Event.
Penalties
Purchasing health insurance is strictly optional; however, there are consequences to canceling a health insurance plan when employees opt not to replace it with another plan. People choosing to opt out of health plans (self-insure) may have to pay a fine when they file their income taxes.
Helpful Links:
Cancel Your Marketplace Plan – Healthcare.gov
Exemptions from Healthcare Fee – Healthcare.gov