My house has Legrand outlet boxes for coaxial cable -- they appear to be these. I would like to run ethernet to these cable boxes, since there's space for additional cables in the box. However, I'm not sure how I would get the cable to go into the box since the mounting nails appear to be in place and I don't want to remove any drywall. Is there any way to remove the box without breaking it so I could grab the new ethernet cable from the wall?
This is fishing. You can usually slice a little bit of drywall from the area above the box and stick an electrical snake in there and try to snag the cable and direct it over to one of the access points on the box. You can also loop the cable before running it in the wall and then try snagging it through one of the access points into the box. Sometimes you just have to cut the the nails with a hacksaw blade, remove the box and then get a new "old work" box that is supported by drywall clamps. Pull the cables into the box and then install it in the same hole as the old one.