Why not reset the monsters to the level of the players? Many games I've played use dynamic monster levels. When you start out you're fighting wolves with 50 to 100 hit points. As the game progresses you're much higher level but the wolves you fight may have 300 or 400 hit points, still easy to kill but they are different than one ones you began with.
Another option may be to not have stats change very much. In systems like D&D there is an initial spread of 3D6 (3-18) for the base with a cap of +5 bonus maximum. While they may get better equipment over time, and gain a handful of hit points or abilities with each new level, having a freshly rerolled character after another has died will have some impact with a party, but generally not so much that the game is destabilized.
Consider it in both directions. It isn't that fun to have leveled up and suddenly have the old monsters fall down dead at the sight of you. It also isn't that fun to have someone leave and suddenly the world is destabilized because your party is too weak.
I know many games love to make leveling up and adding stats into an enormous event: increase the stats by 20%, 40%, or even more! If adding 6 hitponits per level is good, then adding 60 hitponits should be better, right? The problem is you develop god-like characters far too quickly. While it can serve as a gate and encourage level-grinding, it doesn't really serve stories and narratives well.