There are reasons why one might want a year beyond 9999. For instance, if you are calculating astronomical events, you might want to know the next 1,000 times that Halley's comet will return to earth. Or, if you are fascinated by arcane religious calendars, you might be amused by the cycles of Jewish holidays through the seasons, or how often Ramadan starts on Christmas.
Unfortunately for this purpose, most databases where designed with business needs in mind, not astronomy or archeology or other domains. If you really need dates beyond the range, I would suggest setting up your own calendar system. One method is to create a bigint
column and count the number of days since some canonical date, such as '0001-01-01'. Another is to store the dates as strings in a 'YYYYY-MM-DD' format.
Or, perhaps you just have a typo and 1999 is sufficient.