I have Medicare part ‘A’ and Medicare part ‘B’ insurance, and between them they pay for most of my medical expenses. I get about 80% of my prescription charges paid by Medicare part ‘B’. I work in data processing. I am a contractor and my specialty is Health insurance, and I have found that as I move from state to state on different contracts, I have to be careful to inform my insurance provider, because not all providers have coverage in every state. That’s briefly what Medicare parts ‘A’ and ‘B’ do.
Now, let's examine supplementary, so called Medigap insurance, which several companies offer to cover the gaps, i.e. expenses that are not covered by Medicare ‘A’ and ‘B’ combined. While it is prudent to consider so-called ‘Medigap’ insurance, you should not assume that all of your expenses will be covered.
The additional benefits are for payment for medical expenses excluded by Medicare's deductibles, such as limitations on approval of charges, or limitations on length and type of care in nursing homes, and by other limitations. It is important to note that most of these policies pay substantially less than 100% of the expenses not covered under Medicare. Insurance companies that sell Medigap policies can exclude preexisting conditions for no more than six months. The National Association of Insurance Commissioners limits Medigap to 10 standard insurance policies, and each policy must provide a basic amount of benefits.
However, this does not mean that you will not receive a bill.

Are you asking if they should be receiving a bill for their Medicare A & B and supplementary insurance or for medical care from a doctor or hospital? There is no charge for Medicare part A for those who qualify. Part B has a charge of about $99 per month that is usually deducted from one's social security check. There is a charge for almost all supplementary insurance plans that varies by plan. The coverage of the supplementary plan also varies.
With 'straight' Medicare part A and B, the person usually pays about 20% of the Medicare approved amount for medical charges, so a bill would apply. Medicare also sends reports of what they have paid and what the individual is responsible for - so it is a good idea to wait to pay bills until you have seen that report.