Subtracted/hidden part becomes new mesh

I would propose a sculpt tool feature which would

1. extract any part of the mesh which is subtracted from original mesh
2. it would separate any part of the mesh which is box hidden

The first 1) feature would operate as separate subtract brush on left side panel in sculpt mode.

Second 2) would be just box hide tool but it would have an action/operation to separate hidden part of the mesh. This action could have an thumbnail left from box hide tool.

Idea came from: Link: Hide tool showcase video