You can almost be sure its a part of the vertical advance shaft from your description and rest assured the bike will run much better with the KIPS valves working. Like CC said its the result of either not supporting the shaft or not realizing the nut on top the shaft is reverse thread (left hand). Count yourself lucky, often the snapped of piece of the shaft get punched through he clutch cover, case or rips the clutch basket to threads.
To check and see if the kips system is working: have a look at the throttle side of the engine, you'll see where the vertical KIPS shaft run up from the clutch cover and into the engine. You see the rubber boot between the gray plastic cover and the aluminum casting? Pull it down from around the plastic cover to expose the shaft. You should see the shaft rotate at around 6000 rpm.
You wont hurt the bike running it with the KIPS valves disconnected but you'll be missing out on either lots of bottom or mid to upper rpm power depending on where the valves are sitting. I'm assuming you've got all the loose pieces out of the engine or yea you could catastrophically damage the engine.