When an avoidant finally realises you do not care anymore

You know the pattern well, if you have been with a dismissive or a fearful avoidant. They hold back. They pull away. They put space between them as you pursue, clarify, and struggle to be near. That cycle may take months or even years.

Something becomes different as soon as you cease. The instant your energy will not follow them, protect them, or await their coming back. Once the avoidant feels like you really do not care anymore, and they know that it is not a gimmick, the relationship dynamic may change in a manner that would surprise both of you.
This is what that turning point is and why it is important and what it means to your life.

How evading was based on your nurturance.

Avoidant individuals like distance to experience safety. The distance makes them stay in control. When you care too much then that control remains in place. The fact that you have their attention tells them that they can draw away and still have you. When they do not give much, you cannot give less. That pattern reassures them.
Once your behaviour no longer fits that pattern, they become unsafe. Your silence substitutions of explanations. Your calm replace pleading. The script is no longer familiar. That is unsettling.