Measure the width of the refrigerator. Add the clearances recommended in the appliance’s paperwork to the width, and measure this width at both the top and bottom of the the wall. If the refrigerator needs a clearance of 2 inches on each side, for example, add 2 inches to the width measurement.
Run a stud finder over the surface of the wall between the width marks to find the studs. Mark all of the wall studs in the space.
Turn off the electricity in the room by flipping the breaker in the breaker box or pulling the fuse in the fuse box. Cover the floor and fixtures in the room with plastic sheeting. Tape the sheeting around the fixtures and the floor with masking tape.
Hit the section of the wall that you want to deepen with a hammer between two of the wall studs. Use the hammer claw to peel back the drywall around the original hole that you made until you have removed most of the drywall from the area.
Redirect any water pipes and wires that lie inside the area of the wall that you want to deepen. Move pipes outside of the area into which the refrigerator must push back. If you have never moved plumbing pipes, hire a plumber to accomplish this task, or you may end up with water issues. If you have no experience with routing electrical wires, hire a professional electrician to avoid injury and damage to your home.
Cut the rest of the drywall away with a drywall saw to ensure a straight cut at the sides from the top to bottom of the opening. Cut through the center of all of the studs in the opening in the drywall and remove the top portion of the stud by pulling and twisting the piece until it comes free from the top plate. Repeat the process with the bottom portion of the stud until it comes free.
Measure the height of the opening from the board that runs horizontal across the bottom of the wall and the board that runs horizontal across the top. Cut two, 2-by-6 boards down to this length. Install the boards on either side of the opening in the wall so that the inside edges of the boards line up with the wall opening. Secure them with wood screws drilled in at a 45-degree angle into both the top and bottom plates to create replacement joists.
Measure between the two replacement joists you installed on either side of the wall opening and cut two more boards down to this size. Install one of the boards at the top of the opening against the top plate and one of the boards against the bottom of the opening against the sill plate, securing them into place with screws at a 45-degree angle. If the bottom plate sits higher than the level of the floor, sand it down to ensure that it sits even with the floor so that the refrigerator will slide back into the opening.
Cut down drywall pieces to fit over the back of the wall opening and the sides of the opening. Secure the drywall pieces in place with drywall screws. Apply joint compound into the cracks between drywall pieces to make a smooth surface, and allow the compound to dry before painting or covering the drywall with any other covering.