A roll cage is usually described as a safety device, and it is, but it is also a structural member welded into the car. Both roles follow from the same set of load paths.
The cage works by giving loads somewhere to go
In a rollover the roof structure of a production car is designed to support a specified load, sized for a road accident rather than repeated competition impacts.
A cage replaces that job with a tubular framework running from the floor at the front, over the occupants and back to the rear suspension mounts.
Loads applied at the roof therefore travel down the pillars of the cage into the strongest points of the shell, rather than folding the production roof rails.
Triangulation is what makes tubes stiff
A rectangle of tubes can deform into a parallelogram under side load. Adding a diagonal makes it a pair of triangles, which cannot change shape without the tubes themselves stretching.
Door bars, harness bars and rear braces all serve this purpose, and sanctioning rules specify their geometry rather than leaving placement to the builder.
Joints matter as much as tubes. A weld that concentrates stress at a small area can tear the mounting plate out of the floor rather than the tube failing.
Mounting plates spread the load into thin steel
Vehicle floor pans are thin sheet steel and cannot accept a tube directly. Cages are welded to plates that distribute the load over a larger area.
Where possible, plates are placed on both sides of the floor and joined, so the load is carried in the sandwich rather than by the welds alone.
Rules commonly specify a minimum plate area and thickness for exactly this reason, since an otherwise correct cage can fail at its attachment points.
Stiffness changes the handling as a side effect
A caged shell twists far less between the front and rear suspension, which means the suspension geometry stays closer to its design values under load.
That usually makes the car more responsive and more consistent, but it also means spring and damper settings developed for a flexible shell no longer suit it.
Drivers sometimes report a car feeling harsher after caging, which reflects the chassis no longer absorbing motion the suspension is now asked to handle.
Why cages belong in competition cars
A cage places hard steel tubing close to occupants who must be restrained by a harness and protected by a helmet and padding to make that proximity safe.
Without those, a cage can injure an occupant in an impact that a standard interior would have handled, which is the reason the elements are specified as a package.
Sanctioning bodies therefore approve cages alongside seats, harnesses and padding, and inspect the combination rather than any single component in isolation.