A rehearsed farewell can become useless when the real face appears.

Rehearsal prepares words for an imagined version of a moment, and the imagined version never has the actual person in it. When they are in front of you, breathing, with their own face doing something you did not plan for, the script goes. That is not a failure of preparation. It means you were genuinely there rather than performing something written earlier.

If the words go, let them. Say the simplest true sentence available, or say nothing and stay. Almost nobody remembers what was said at a goodbye; they remember whether the other person was really present for it.