Assuming the company found the electronically signed contract, they would then need to file in court to come after the money. At minimum, that would be 10-20K for lawyers to be retained, have you served papers, file, etc. I don't think they will go through the legal system to recover. Someone mentioned you suing them, but that would make no sense with lawyer fees, chance of losing, paying their fees, etc. The only person that wins with a lawsuit are the attorneys.
If you don't pay them back, expect to get letters, marks on credit report, etc.. As others have said, having an unpaid debt to Air Wisconsin when a future employer pulls your credit report might just eliminate you from consideration with no chance to explain.