What is the relationship between constipation and incontinence?

Overflow... It seems paradoxical but constipation can lead to a 'solid mass' of stool around which only liquid can flow...Leading to spurious diarrhea than can be difficult to control. This, in turn, can lead to incontinence.
Cause and effect. Severe constipation can sometimes result in impaction which distends the rectum. Liquid stool above the impaction then leaks around the impaction causing leakage and incontinence. This is called encopresis.