The personnummer encodes gender in the last digit (which, IMO, is very silly) - so when that changes, the number has to change too.

Poland has a very similar numbering system, the PESEL. It can change if the date of birth was recorded inaccurately and you need to correct it, or, because the PESEL encodes gender, when you get your gender marker legally changed.

Gender change, incorrectly recorded time of birth, duplicate number (though that one hasn't happened in the last 30 years or so), replacement of a temporary number with a permanent number.

The extreme case is witness protection, but in that case only the police would even know about the connection.