Shelter and exile
When home is in danger, a leader can shelter in an ally's base.
A military ally may let your leader shelter in one of its bases. Ask on the Diplomacy screen, then take your leader there with an army group.
Rival leaders may ask you for shelter too. Saying yes earns their trust, but their enemies will not like it and may demand that you hand them over.
A rival leader in exile plays it safe: their nation defends itself at home but makes no new moves abroad.