Modulo vs Scaling vs Capping when performing filters
When doing a filter operation such as a blur, in many cases the filter itself will be normalized so its values sum to 1.0, precisely to avoid this problem.

In cases where out-of-range outputs do need to be handled, the most common way is what you called capping. In graphics it's more commonly known as clamping or saturating. This is the default behavior if, for instance, you run a pixel shader on a GPU and output out-of-range values.

Renormalizing the output image might be necessary in some special cases depending on what you're doing. I can't think of anytime that I've seen the modulo behavior used—it would be a pretty weird operation to do on a visual image.