The best example of a non-tripping chine I can think of is the basic Sampan hull. There are 2 chines (turns or knuckles) in the area of the bilge instead of one. The hull between the 2 chines is typically about 45 degrees and as the boat slides sideways in a turn or on the face of a wave the shape of the double chine hull allows the water to slide transversely under the hull (especially aft) without causing extremely high lateral resistance very low that could capsize a hull especially abeam to breaking seas.
Yes the keel can have a similar affect depending on the size of the keel and how that keel can/could push the lee chine down and increase chine tripping probabilities. Or if the chine is soft like a lobster boat then the keel would be mostly what could cause tripping. This is one of the best features of the soft chine. But in a sharp turn a soft lee chine tends to pull the inbd chine down and the result can be over banking. I practically fell out of a soft chine OB w no keel because of that.
North Western Washington State USA