The simple answer to this question is that you will lose the benefits of the plan and be faced with paying your medical expenses out of pocket. If your insurance is expiring due to a loss of employment or layoff, you may be eligible for COBRA to extend the coverage for another 18 to 36 months. This option will require you to pay the full cost of premiums, including any portion that had previously been paid by the employer.
For all other situations, you will need to find a replacement coverage policy, sacrifice proper health care, or pay the costs yourself. Group policies have the most lenient enrollment plans, but people in good health may qualify for the lowest rates through an individual health insurance plan. It is much better to acquire new insurance before the original coverage expires, as lapses in coverage can be expensive, and most insurance plans have a mandatory waiting period before they go into effect.
You may also want to investigate government sponsored plans to find out if you are eligible for all or partial coverage. Medicare and Medicaid are only available to people who meet certain qualifications, but those requirements include such things as pregnant women and the elderly. In fact, enrollment into a government-sponsored health plan may be a requirement for some pregnant women to receive additional assistance.