Writing this once so I can stop repeating it across threads. It is about constipation and the lower-GI picture, and it is deliberately narrow — everything I am not confident about is marked as such.
What is actually established
The mechanism is slowed transit plus reduced intake, and that combination determines which interventions work. Less food means less bulk, slower motility means more water reabsorbed, and the result is a smaller, drier, slower stool. Insoluble fiber adds bulk to a system that is already moving slowly, which is why it frequently makes things worse. Soluble fiber holds water and is the better first choice, and an osmotic agent works with the mechanism rather than against it.
The condition it depends on
One important qualification: fiber without adequate fluid is worse than no fiber. If intake is down, fluid is usually down too, and adding bulk to a dry system is how people end up in real trouble.
The practical version
Soluble versus insoluble is the distinction that matters: psyllium and oat beta-glucan hold water; wheat bran adds bulk. On slowed transit with low intake, the first helps and the second often does not.
What I am not sure about
The narrow version of the question is what the mechanism is, because if it is transit rather than water then fiber is the wrong lever. I have searched first, so if this is covered somewhere point me at it and I will read it.
— kevin_tulsa · corrections welcome and will be edited into this post with credit