The most interesting part of this theory is what we could do after expanding the asteroid with the mesh bag.

Once you have expanded the asteroid with the mesh bag containing all the debris, you can then harden the surface any way you want. If you harden/encapsulate the outside surface first with some material (like: steel/iron/concrete/plastic/glass) then harden the interior after removing all the useful deposits of material, you can have a fully functioning bubble of atmosphere to work with/build with to create a small city.

Add a landing platform w/ tunnel to get through the barrier and boom you have a fully functional city.

You can then hopefully take the carbon fiber mesh bag and use it on the next asteroid that fits the criteria or use a carbon fiber mesh bag as an easier way to mine useful resources out of asteroids.

Most of the above can be done with robots once we start expanding into space.