I think there are a lot of problems with how this type of scenario is both viewed and handled. From personal experience and a lot of things I have read and heard from others the most typical way this is handled is the therapist is expected to “refer the client” and terminate all contact. While the therapist has training and will have professionals to help them handle this transition, the client does not. You were their trusted professional and then things are being terminated entirely on the therapists terms when they already hold all of the cards. I do not understand how therapists do not see that this is an abuse to the client.
if you are, in fact, a therapist that is in this situation PLEASE DO NOT handle this, likely vulnerable and caring, client this way. You became attached for a reason and that reason likely speaks to some very admirable qualities of that client. Don’t destroy those with the false pretense of “you are no longer helping them, therefore you need to terminate immediately.”

I might suggest actually giving the client some credit and talking to them about this. Explain and then help them transition out. Be open to meeting with them and their new therapist. Treat them like they are an intelligent human, and because you “accidentally” developed an attachment you really should acknowledge that you were/are using them to some extent and/or a type of mutual relationship has developed. Don’t use and discard your client; it’s very likely a problem they have come to you for therapy for in the first place. If you “terminate immediately” and entirely on your terms, that is absolutely the worst form of using and discarding a person since you are their trusted and paid for safe place. Please do not cause or perpetuate that kind of harm. It does not end well for the client. Help them transition out or acknowledge the mutual relationship that has developed and TOGETHER decide what can and should happen there.
to me this seems so common sense obvious