> they said that it seemed like I never actually properly entered the system, but had just began

Can be quite a risk for people who entered a long time ago.

https://en.wikipedia.org/wiki/Windrush_scandal

> Bureaucracy can be crazy at times, and sometimes it seems like data just gets lost, for whatever reason.

The easiest way of reconciling data with reality if the rules don't allow changing the data is to change reality. By deporting people.