It is a very sad day when you are moving puzzles and one slips out of your hands and spills out onto the floor.
This isn't too bad if it is just one puzzle and it is in your home. You can simply pick up all the pieces and hope that none get missed because they went under some bit of furnature. To prevent spilling and lost pieces, you should always put your puzzles in zippered baggies for storage and shipping.
We have found that puzzles up to 2,000 pieces often fit into a single zipper baggie, but they can get a bit bulky starting at about that size and moving up. On the larger puzzles you may find it best to use multiple baggies to get things to fit back into the box properly.
By storing puzzles in zipper baggies, you prevent the pieces from spilling if you drop a box. But more importantly, when shipping, the pieces won't escape the box, especially if somehow the box is damaged. Or if you are shipping multiple puzzles in a single larger box, no pieces will get out and mix.
This sounds unlikely, but we have seen it happen where pieces are free floating inside a larger box and that box may not be sealed perfectly. A piece can end up under a flap or escape the outer box all together and get lost forever.
So when you are putting that puzzle back in the box, just toss the pieces into a zipper baggie, remove as much air as needed to get the lid to close properly and be confident that none of the pieces will go missing later.