(lay)orders that make a promise of obedience to the bishop


My priest told me that when he was younger and serving as a priest in Africa, he came across lay orders that, instead of making a vow of obedience, made a promise of obedience to their bishop.
I have only heard of one religious order who does this but I never heard of lay orders or lay people who are under the obedience of the bishop by promises.
Also my priest told me that if there are no religious order that are willing to admit me or if I dont find an order that suites me, we can invite the bishop and that I can make vows anyway.
I never heard of this before. I though that this was only possible in the context of joining a lay order. Could anyone shed some light on this please?


Consecrated virgins make vows but do not belong to a religious order.



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