The answer is in your question.

 1. Convert polygons to lines (features to lines)
 2. Merge them with fault line
 3. Dissolve output from step 2 into **single** part polylines
 4. Select and delete from DISSOLVED lines that share line segment with FAULT line

RESULT:

[![enter image description here][1]][1][![enter image description here][2]][2]


NOTE solution applicable for topologically correct geometries, i.e. fault lines truly follow boundaries and there are no slivers/overlaps in polygon layer.

Some manual editing possible, consider fault line going up a bit from uppermost point.

  [1]: https://i.sstatic.net/PCAN7.png
  [2]: https://i.sstatic.net/GAEoK.png