Dang, that's a good question...of course, the "student" answer is "You don't."
All I can think of is a very diabatic system, like the thermal homolysis of a weak bond where the product barrierlessly rearranges into something else. The "something else" would be very different from the TS, even if it were high-energy, and thus violate HP. Maybe something like a thermal nitrene formation from azide, which rearranges into a seven-membered aza ring? That might have a local minimum on the nitrene, though...