No, a country is just a landmass, and when "Japanese become the minority" that would be a problem solved (the problem being entitled people from outside the country wanting in).
- Japan becomes an almost empty and stateless or only having a nominal state, landmass with very little population and no functioning economy (no transport network, no electricity grid etc). Unlikely - it's climate is too good.
- It gets militarily taken over as soon it's too weak to defend itself. Likely but undesirable because you don't get to pick who takes you over and that will be by definition someone hostile.
- Immigration and replacement. This is the most beneficial of the realistic options. Because you get to pick the people who replaces you.
Let's see birthrate forecast graph by govt https://pbs.twimg.com/media/E2zKUeHVoAA3ufi?format=jpg&name=...
Oh, but buckle up my friend, because Japan isn’t an outlier. It’s ahead of the curve for a majority of the world’s societies.