This is a common thing, you are certainly not alone. I think there is some anxiety involved in the idea that if you get better then you're going to lose the current relationship. And when it ends, there's obviously some grief in saying goodbye to the therapist. It's essentially similar to other close relationships you develop with select others.

Sometimes there is enough time that you can do this slowly and process it well. Sometimes it is not so. For instance it could happen that the therapist might die or develop a serious personal illness or be forced to move far away for whatever reason. Usually they will do their best to transfer the person's care to another therapist they're familiar with. But it's not so easy for the patient because it's not like you can extract the relationship and transfer it to someone else as if it was an object. That original relationship took a long time to develop.

Luckily the above doesn't happen frequently. I think another thing that many good therapists do is try to get the patient to develop good, close, and "healthy" relationships outside the office. That way, "losing" the therapist will feel less damaging and painful. Because for someone with no reliable supportive relationships out there, losing the therapist, even if as a result of patient's general improvement and better mental health, can be almost traumatic.