They can still say they spent money on you if they have done anything to prepare to train you, I.e. pass up another person for training, set up sims, prepare paperwork and materials. I'm sure there is a lot more they can say they did in preparation for your training you failed to show up for. And they have paperwork you signed agreeing to reimburse them for training costs should you leave before the set amount of time.
But since you never received any training from them it is highly likely nothing will come of it.