Debris and dropped stages
Nothing you drop is deleted. A separated stage, a jettisoned shell and a part torn off in a collision all keep flying under their own weight, their own engines and their own air, and some of them end up in the world as ships of their own.
What a dropped stage is
Fire a separator, a decoupler or a docking port and whatever comes off becomes a piece: a ship with nobody at the controls. It still has everything it had a second ago. Its tanks feed its own engines, its own parts still run, and gravity and the air treat it exactly as they treat you.
So a solid booster dropped while its grain is still burning flies on under thrust until the case is spent. A liquid stage dropped with its engine lit burns at whatever throttle it was on when it left. A parachute that was already open keeps dragging. What a piece does not have is a hand on the controls: it will not turn, it will not stage, and its throttle is frozen where you left it.
A strap-on booster is the usual offender: the Decoupler gives it only a small push, and an empty case in the airstream can swing straight back into the stage it left. The Separation Motor is the answer, a one-second solid cluster bolted to the booster's flank that fires as the booster lets go and shoves it straight outward. Throw a booster clear has the placement.
Debris is solid, and it can hit you
A piece is not scenery. If it touches your ship, or another piece, the two collide: the blow shoves both of them and sets them turning, and how hard it hits depends on how fast they were closing at the point of contact. The parts under the blow on both sides are judged on the load it gave them, against each part's own MAX G figure. A gentle drift back into the stack is a nudge and nothing breaks. A case ramming you at thirty metres a second breaks whatever it struck, and a piece that loses parts that way falls apart into whatever still holds together.
The ones you can fly
A piece carrying a Command Pod, a Crew Capsule or a Sat Controller can be taken over: a switch button appears in the flight and control jumps to it. A piece with none of those has nobody aboard and nothing to steer with, and is simply debris. See Switch to a dropped stage for the button.
A piece that stops pushing becomes a ship in the world
The moment a piece is coasting in space, above the air, with nothing pushing it, the world takes it: it gets an entry of its own, with a name and a card on the map, and it goes on orbiting whether or not you are looking. A flyable piece is named after the ship it left with a number after it. One nobody can fly gets the ship's name and the word DEBRIS.
That only happens once nothing is pushing it. A piece still under thrust has no settled orbit yet, so it waits until its burn is over. Leaving the flight while a piece is still burning shuts its engines down first and stores it as it is, because nothing burns while you are away. A piece still in the air when you leave the flight is lost.
Anything that reaches the ground is gone
A piece that falls all the way to the surface breaks up and disappears, unless it carries a command part. One that does parks where it landed and stays there, and you can still switch to it while the flight lasts.
None of it is worth anything to you. Recovery pays for what is still aboard the ship you bring home, and a stage you dropped on the way is not aboard. See Landing and recovery.
Fairing halves and broken-off parts
Staging is not the only thing that makes a piece. Jettisoning a Payload Fairing splits the shell into two half-shells, and those are flown like anything else: each is blunt to the air whichever way it tumbles, so the pair falls behind the rocket rather than chasing it, and they break when they land. Parts knocked off in a collision or an explosion become pieces the same way. Whatever comes off, the rule is the same: it is still there, it is still solid, and nobody is flying it.