Redundancy in wood framing significantly adds to its resilience. Though not all holes drilled into walls land on studs and the interior cladding, like sheetrock, is surprisingly strong. That cladding adds to the wall's strength.When a wall is damaged, there are a number of remedies that don't involve replacement of the stud. They include:
The practice of "sistering" joists or studs when an existing structural member loses its ability to maintain rigidity by itself. Sistering involves fastening a new structural member to an existing member.
Notching and blocking is another common technique that can be done to a damaged area, often seen in plumbing applications when it would be impractical to drill a hole and pass a pipe. There are special circumstances where notching and blocking are allowed depending on the situation. A notch can be cut out and have a block installed tightly on portions of objects under compression. It is not uncommon to see notching and blocking paired with sistering, bracing, or blocking to other existing structural members as described below.
Bracing is another repair technique which will involve sandwiching a compromised structural member between two other like structural members, or by using blocking between the compromised structural member and another structural member. Bracing can be done on objects experiencing compression or tension. Bracing is common in prefabricated roof design and also in deck construction and floor truss systems.
There is laminating which is similar to bracing or sistering but involves building up layers. It is often done to prefabricated truss systems that have received modification or repair where pieces of structural plywood are fastened to either side of a joint on a truss. Adding cladding to the side of a house is a form of laminating as the outside cladding, usually known as "sheathing", and inside cladding like sheetrock, make up layers of a wall adding to it's rigidity.
Binding or strapping can be used for repair. It involves wrapping a rope, wire, or cable around a splintered component, or can be used as a method of attachment when bracing or sistering. Strapping is often used when tying large beams together such as in log cabin homes, or fence posts. It is very common in prefabricated roof trusses, and diagonally on walls needing stiffening or lacking rigidity.
Adhesives added to splintered framing members is another repair. It is usually done with a mechanical method above, however it can be used by itself in some situations.
More care must be taken in load baring components than just partitioning components. Modern residential framing often involves using boards that are spliced (tenon cut and glued) together in non-load baring applications such as in partition walls where resistance to shear forces and horizontal deflection is not structurally significant.
In 15 years as a framing and remodeling carpenter I've only replaced a couple of studs due to fastener damage in residential situations that had television mounts improperly installed. Most structural repairs I've done have been due to water damage over time followed by animal action. The latter usually leading to water damage. Insects do do damage in Minnesota where I live but usually are present after water damage has occurred, or rodent activity was present. I have done a couple of repairs to fire damaged structures, and one vehicle building collision.
A dock truck needing a 14' high door drove through a 12' high door taking the header and header support posts (3 studs laminated together) with it on the gable end of the building. Despite a 14' high by 12'9" hole made, there was no detectable damage to the gable truss, roof, or surrounding framing. This was in Minnesota in the winter and there was easily a foot of sitting snow on the roof. It even ripped a copper natural gas line that was attached to the header without breaking it even though the gas line was holding a good amount of the header weight!