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I have an arguement for the regiment to return to its home province.

Much of the Regiment would be the Barons, Baronets & knights of the province, together with their retainers. When their province is fallen and they hear about it, many would want to return home to be able to swear fealty to the new lord in order to keep their lands, particularly if they felt their current liege has no way of restoring their lands to them.

It's not instantaneous, and can rely on an evaluation of power between the 2 sides, as well as reputations