I can't recall how this works. When you have a card attached to a target, and the target gets destroyed, does the attached card automatically get destroyed as well, or does it depend on the card text?
Case in point: I was playing The Dreamer with Chrono-Ranger, and put "The Ultimate Target" onto one of the projections. When the projection died, the bounty remained. There's nothing on the card text indicating the card should be destroyed when the target leaves play, not like the other bounties. Oversight? Bug? Intentional?
Playing the cardboard game, my intuition always told me that if there wasn't a target next to an attachable card, it ought to go away. But with TUT, it's actually useful to keep it in play; if it's your only bounty, you can still get use out of the Masadah and Danny Boy, if DR is an issue. Granted, it still seems like a weird thing, but that's the only reason I can see for it staying in play. (Unless we want to get into discussions of it being his "best" bounty.)
When they bring WotC to the video game, you'll see that Sky-Scraper's links stick around after their assigned targets are destroyed. This comes in handy for having a bunch of extra links in play for Explosive Reveal.
It's also slightly relevant for Expatriette, in that ammo can be left behind if the gun it's attached to is destroyed. But there are exactly zero cases in the game where you would want to destroy a gun before destroying its ammo, so this rarely comes up.
A similar case can occur if a gun is destroyed with ammo attached. The ammo stays in Expat's play area not doing anything. Sky-Scraper also has Link cards which stay in play even if the target it's attached to leaves play.
As far as I remember from playtesting, the reason for leaving that text off was partially that fitting the text on the card was tricky, and partially thematic - it's the ultimate target, after all, so it shouldn't be being thrown all over the place as easily. Plus it still powers Hunter and Hunted, Masadah, etc. which is gravy.
There's also Infection cards - if a hero gets incapped whilst Infected, the Infection doesn't go away, so that hero can keep beating up their friends via Afflicted Frenzy. Yaaay :P.