Disclaimer: None of this is my own ideas, and I take no credit.
Libahunt posted a instructable under the title "Little trick for desoldering through hole components" and fred3655 and others offered more suggestions.
Libahunt's idea is that you use a rubber band under tension attached to a hook to pull free through hole components when you desolder them. Fred3655 suggested using a clip of some sorts to prevent the flying components from getting away.
I quickly made the mock-up on the photo to try to illustrate both of their ideas. In the picture the PC board is positioned so that you can see the arrangement of the rubber band and crocodile clip, but of course you would have to reposition the board to reach beneath for desoldering.