I guess finished means completely outworn.
This sounds like a seized caliper on that side, which always brakes a little and so wears the pads.
It does not have to brake that much that you notice it, but typical signs are a hotter wheel on the one side compared to the other side after some (especially fast) driving and a wobbling noise which often occurs above a certain speed and vanishes at a different, lower speed. You may also notice that the car pulls to one side of the good brake when braking from high speed.
Another hint: Lift your car and compare how well you can rotate the wheel by hand, compared to the other side.
The caliper can be overhauled, but since this also is some work / money, simply replacing it may be the better option.
(Of course, it could be something different upstream the brake system, but usually, it's a seized caliper)