Many many years ago. I was working on a Tudor day-day when a tiny spring sprung and went flying. It wasn't part of the original ETA movement, but a Rolex part, so I knew I needed to find it or pay Rolex to repair the watch.
I found the part after an hour of searching the floor
What I did was grab a section of Saran wrap and laid it over the top of the movement and my hands and worked through it. When the spring popped a second time. It hit the Saran wrap
That was the only time I did this. Lot more careful now and only lost one small part since then.
Get a large fridge magnet (and demagnetizer). Makes it easier to find metal parts