A resonator is a chamber in the run whose job is to cancel a narrow band of sound that the muffler alone leaves behind. It is not there for flow and it is not there for looks. Removing it does not simply make the system louder; it makes one part of the sound character disappear and another become obvious.
That is why owners are often surprised by the result. The car is not just noisier. It is differently noisy, with a hollow quality at some speeds and a sharper edge at others, and whether that is an improvement depends entirely on what the owner wanted from the change.
The usual approach is to cut the resonator out and weld in a straight length of tube of the same size, so the run continues without a step. Done properly, the bore is unchanged through the replaced section and the only difference is the volume that has been taken out of the system.
Done quickly, with a sleeve and two clamps, the result is a run with two steps in it and a joint that will move. On a section sitting close to the floor, that movement is what turns a sound change into a rattle the owner hears every time the car settles.
A freshly welded section sounds different on the first start than it will a week later. The metal is clean, the packing behind it has not settled, and everything is still where it was put. Judge the change after several heat cycles rather than on the drive home.
It is also worth listening from outside the car as well as from the driver's seat. A change that sounds reasonable inside can be harsh at the tailpipe, and a change that sounds aggressive outside can be tiring at a steady cruise.
The complaint that follows most resonator removals is not volume but drone: a steady, low note that sits on the car at one particular cruising speed and refuses to go away. It is a resonance, and removing a chamber is one of the surest ways to move a system into it.
Whether it appears depends on the length of the run, the volume of the muffler behind it and where the tailpipe ends. That is why two cars of the same model can respond differently, and why a change that suits one owner is unbearable to another.
On a section downstream of the sensors, removing a chamber changes nothing the engine management reads. The car will not run differently, and any claim that it will usually turns out to be a claim about a different part of the system. What changes is the sound.
Where the resonator sits close to a sensor or a flex joint, the welding heat is the thing to watch. A flex section that has been cooked will fail later, and the failure will be blamed on the removal rather than on the heat that went into it.
If the aim is a deeper note at idle and the car is used mostly on short trips, removing the resonator is a reasonable experiment, provided the replacement is a proper butt joint rather than a clamped sleeve. If the car spends its life at a steady cruise, think harder first.
The rest of the system sets the ceiling on what is achievable. A stainless steel exhaust system built as a complete run behaves more predictably than a mixed assembly of parts, and the replacement tube should come from a known exhaust pipe section so the wall matches what it joins.