Medicare has strict rules for enrollment. Most seniors are automatically signed up for Medicare Part A, the portion of the program that covers hospital care, when they turn 65.

Enrollment in Medicare Parts B and D — which cover physician services and prescription drugs, respectively — can be delayed if a person is still working and covered by an employer-sponsored plan.

However, the enrollment process for those who delay can be confusing — and lead to costly mistakes. Here are some seniors who suffered from those mistakes.

One is a 67-year-old schoolteacher who delayed enrolling in Medicare Part B to ensure that his younger, ailing wife could keep the same health coverage.

Another is a cancer survivor who, having met her deductible under her employer-sponsored plan, wanted to complete her chemotherapy regimen before switching to Medicare.

Then there’s the widow who found herself uninsured for months after not moving quickly enough to sign up for Medicare Parts B and D after her husband’s death.

All of these seniors decided to delay enrollment in Medicare Parts B and D to stay on their employer-sponsored insurance under the terms of a law called COBRA, which permits people to extend their health benefits after leaving a job by paying the premiums themselves.

Unfortunately, all three seniors also ended up facing significant financial penalties and delays in securing Part B coverage. That’s unfair and must change.

The number of seniors subject to this COBRA trap is growing. Seniors have surpassed the young and middle-aged as the fastest-growing segment of the workforce. They now account for over 16 percent of U.S. workers — up from 12.1 percent in 1990.

For working seniors with employer-sponsored plans, it may make sense to delay enrollment in Parts B and D to avoid paying premiums for coverage they don’t yet need. Others may defer enrollment so a younger spouse can stay on an employer-sponsored plan.

Medicare allows seniors to delay enrollment without penalty if they have coverage through work. But once they retire and coverage ends, they have a small window to enroll in Medicare Parts B and D without incurring fines.

If they miss that window, they could face late enrollment penalties of 10 percent for every year late — and have to pay higher premiums for the rest of their lives. They could even be left without insurance while they wait for the next sign-up period.

The open enrollment window closes even faster for seniors who keep their employer-sponsored coverage through COBRA.

Medicare does not recognize COBRA as “creditable coverage” — that is, coverage as good as or better than Medicare. So a senior who continues his or her workplace coverage through COBRA begins racking up late enrollment penalties almost immediately.

That makes little sense. The only difference between employer-sponsored coverage and that obtained through COBRA is who is paying the premium — the employer or the former employee.

Medicare has its reasons for these rules. Limiting enrollment periods to a few months annually and imposing late penalties discourages patients from waiting to sign up for coverage until they’re sick.

But the seniors using COBRA are not looking to cheat the system. They’re still paying premiums on the plans they were covered by through their employers.

At most, they made an honest mistake — one for which they’ll pay for the rest of their lives. And it’s a mistake that will grow more common as seniors work later in life — unless Congress dismantles this COBRA trap.

Janet Trautwein is CEO of the National Association of Health Underwriters.

By Janet Trautwein