How they would get their money back would depend on the circumstances. Some airlines require a bank guarantee. If you broke a contract and owed them money, they can seek recovery through the courts either in their own jurisdiction or through the defendants if that person has fled.
Most airline companies will expect and stipulate that you have the right to travel unrestricted worldwide. Obviously it has the potential to cause them enormous difficulties if you are likely to be arrested on arrival in any country, for a previous violation history in that country. In addition as has already been pointed out, most employers would expect to be able to secure satisfactory references from your previous employer. This is unlikely to be forthcoming if you have absconded owing them money, or otherwise breached your contract.
It is very unwise to blot your copybook in this industry and to be perceived as flakey or unreliable. There are too many people chasing the best jobs (every job these days,) for airlines not to be choosy in who they select. In an industry that seeks to employ adults with integrity and a mature attitude, you would be at a great disadvantage if you were unable to portray yourself as such.