Good observation and question :) Clipping preserves the range of intensity values but can lead to a loss of detail and color distortion. It affects the overall color balance, especially if one or more components are frequently clipped. We typically have two situations here. The first one is an uniformed adjustment. If the brightness adjustment is uniform, the color balance is generally maintained unless clipping occurs. When clipping does occur, the affected color channels will saturate, altering the hue and saturation of the resulting color. Then there is non-uniform adjustment. When different components are clipped to varying extents, the color balance can shift.

There are ways how to handle and avoid clipping, the solution is actually quite simple. Normalization for instance. By normalizing pixel values after brightness adjustment we ensure they remain within the 0-255 range yet maintain the overall color, so we would not use clipping at all. Generally speaking, as you mentioned in your example, we would increase all values by one. Like adding a constant to the values of a list.