It's not regardless of stability, but it's contextual. The stability of the owner determines which cities can be part of the respawn. If the owner is unstable, all cities are included. If the owner is shaky, it includes the potential capital, core cities, and colonies (from the current owner's perspective), which is still almost all cities. At stable, the capital is still included. All these thresholds are after Nationalism has been discovered, before Nationalism they are one level higher each.
Note that due to other respawn conditions, a minimum number of cities needs to be part of the respawn for it to proceed. So the situation that only the capital is included usually isn't significant for the respawn to succeed, but it can be for civilizations with a small respawn area, e.g. Korea or the Netherlands.
Note that due to other respawn conditions, a minimum number of cities needs to be part of the respawn for it to proceed. So the situation that only the capital is included usually isn't significant for the respawn to succeed, but it can be for civilizations with a small respawn area, e.g. Korea or the Netherlands.