Training Bonds
All depends what country you are in. If in UK; if you signed a bond prior to doing the course, probbaly not a leg to stand on. The bond will probably have a clause in it somewhere that gives the co the right to deduct from pay.
In the case that the co is laying you off, that's different. It would be up to you or your reps to negotiate cancellation of your bond in your redundancy package, or alternatively, the bond may be worded such that you don't pay in the case of redundancy.
If you were issued a bond to sign but never did, unless you objected in writing, you are deemed to have accepted it.
If you are leaving of your own free will, my advice before welching on a bond would be; work out how long it would take to earn that money at your new employer (if you are going contracting, not long), and bite the bullet. If you walk without paying, you are peeing off the company and, more importantly, a manager. This industry is so small that one day you will come up against that man again somewhere. I know, I am in that situation now, but fortunately for me, the guy who was my manager, is about to be my underling.