Yes, there are pet doors that goes through the wall of a home. Understand that walls are thicker than doors, so the thru-wall version is a different product than the thru-door version. Pet doors also come in different sizes, given the size range of pet breeds that people own.
Understand that there can be electrical and plumbing in a wall and you won’t know this until you open the wall. Always cut through the drywall on the interior of the home first, so that you can assess any obstructions in the wall. If you must move the location of the pet door, drywall is much simpler to repair than a hole on the exterior of the home.
