Is this an Insulated Concrete Form house? If so, a channel can be made in the foam insulation for the wiring. It depends on the type of interior finish walls. If you're looking at concrete inside, I do not know what is permitted under building codes as far as making a channel.

Hi, there. It's not an insulated concrete form house. It's a Manhattan apartment building constructed in the 50s with concrete walls, and no foam insulation. I know we are allowed to place the wires in the wall, but we just can't cut through any structural parts of the wall. I guess I was wondering if they could make a channel at the bottom of the wall.

YOU can not do anything with the wiring. An electrian can tell you what can be done. You can get oversized baseboards.

It sounds like they already have an electrician who has cut a channel behind the baseboard - but there are problems with the installation.