Own Provinces and Fortifications in inactive zones will still be working for active users, also all stationed units will still be there defending the object. It's still possible to send units to own Provinces and Fortification, even if they are in inactive zones and you are in an active zone. Call back units from Provinces and Fortification in inactive zones is also possible.
It's not possible to Attack / Raid Provinces and Fortifications in inactive zones, if you are in an active zone.
Tactical advice: Your alliance members in inactive zones could help you win by fighting against your enemies Provinces and Fortifications to weaken their power.
Provinces and Fortifications will be reset after a finished battle royale round.