Death is inevitable.
No, really. If you stand and fight with an enemy for more than a few rounds, one of you is going to die.
I ditched separate to-hit rolls some time ago, but previously allowed a Save to avoid lasting damage when your HP ran out. Because of this, taking down that STR 19 monster could be a case of waiting for it to fudge its Save.
Now, the Save at 0hp is to avoid Critical Damage, which will at the very least incapacitate you. For some monsters, it gives them the go-ahead to swallow you whole or stab you with a deathly poison.
If you pass the Save, you keep on fighting, but the damage still comes off your STR Score. This would be a good time to reconsider how badly you want to win the fight.
This means that superior numbers count for a lot. Into the Odd isn't a martial arts film, where heroes take on wave after wave of enemies. If you're faced with a gunline of soldiers, you probably shouldn't let them get a round of shots off at you. If you're surrounded by a dozen angry cultists, it may be time to negotiate.
Let's imagine that situation. We have a lone, veteran adventurer, Ralf (STR 12, DEX 14, WIL 10, 14hp, Armour 1, Halberd 1d6+1) facing off against four pretty weedy cultists (STR 10, 3hp, Club 1d6).
Adventurer Turn 1: Ralf makes a swing for the lead cultist (5 damage). He's out of HP, reduced to STR 8 and fails his STR Save taking Critical Damage. He's out of the fight.
Cultist Turn 1: All three remaining cultists rush at Ralf with their clubs (4, 2, and 5 damage, totalling 11). Ralf has 3hp remaining, so manages to avoid their attacks for now.
Adventurer Turn 2: Ralf attacks another Cultist for 7 damage. He's out of HP now, reduced to STR 6, but makes his Save to avoid Critical Damage.
Cultist Turn 2: The cultists attack (2, 5 and 0 damage, totalling 7). Ralf is out of HP, so loses STR down to 8. He barely makes his save, so keeps on fighting, despite a nasty wound.
Adventurer Turn 3: Things are't looking good. One Cultist is nearly down, but Ralf is hurt now. The remaining two would stand a chance of killing him next turn, or at least incapacitating him. He could hope they fail their Morale Save after losing half of their members, but it's far too risky. Ralf starts to consider whether he should surrender or flee.
Of course, this would all be different if Ralf had some allies with him. There's a reason that this is a team game, after all.