More than one unique number

The most important property of a unique identification number is that it always refers to just one person. If I have the number than I am able to find the person.

A good illustration is a hospital information system (a HIS). Each patient is assigned a patient identification number.
This is used to couple an operation (or a medical procedure) to the patient.

But what if a patient is in a very severe (and maybe life threatening) situation and is brought to the intensive care unit.
There will be no time to find out his name, let alone his patient number. However the transactions must be recorded. A quick solution is assign directly a new indentification number. If the patient has visited the hospital before than this will be his second number.

So beware: different numbers can refer to the same person.