A Bounty That Never Goes Down
The Number Driving the Entire Plot
Why the Number Exists
Vash is blamed for the destruction of the city of July, an event the anime stages differently than the manga does, and the bounty gets set at $$60,000,000,000 in the aftermath. It's less a reward for a known crime than a planet-wide reaction to a catastrophe nobody can otherwise explain, which is exactly why literally anyone with a gun considers going after him fair game.
The Bernardelli Insurance Society's Actual Angle
Meryl Stryfe and Milly Thompson aren't bounty hunters chasing the reward, they're insurance agents assigned to Vash specifically because his path of destruction is bankrupting their company in claims. Their entire job is damage control, not capture, which makes them one of the few people on the planet with a reason to keep Vash alive and functional rather than dead for a payout.
The Poster Swap
The opening credits quietly track the show's own tonal shift without a word of dialogue: for the first seventeen episodes, a "WANTED - Vash the Stampede - $$60,000,000,000" poster appears in the intro. Starting episode 18, that poster is replaced with one reading "EMERGENCY EVACUATION ORDER." The show is telling you the story just got serious before a single character does.