HC 1 and HC 2 do, they save after your run ends...Does the game save by itself?
In HC 1 you get points after each defeat, and use those point to upgrade yourself, I think the growing is infinite...
In HC 2, you get fame points, they... Serve for you to increase your base stats, and buying other upgrades (like starting with backpack, getting more base gold from each new game, more loot chances from defeating the same enemy, etc), but the skill tree needs to be much, much, bigger to be actually viable, because currently, the old HC 1 system just overshadows it, both are grindy but one rewards you far much than the other one...