Not Medicare, but...

The NCPA reports on a study of Social Security payments going to dead people.

In Southern California and elsewhere last year investigators analyzed 305 Social Security beneficiaries who were recorded as deceased in their Social Security Administration files; at least 140 of them were still alive.
....
On the flip side of the problem, payments were made to dead beneficiaries in at least 88 out of the 305 cases studied by investigators. Some of these improper payments continued for years.

Care to bet Medicare faces similar problems?

Assuming it does...

Private companies get reminders from their insured. Ongoing payments of premiums are "proof of life", and cessation of such payments, although not necessarily "proof of death", are a signal to the insurance company that it should not honor claims from those individuals.

If Medicare's numbers are at all similar to those of Social Security, then we're seeing 88/305 = 29% of payments that should have been prevented, perhaps by spending more on administration. Should this 29% be counted as part of the "overhead"?

Of the 140/305 = 46% of clients listed as dead, some are still receiving their checks. So we don't even know if this poor record keeping is resulting in a net savings, even if we decide we don't care about a failure to extend benefits to qualified recipients.