Pay up
No issue. I left an employer to fly biggish shinyish jets, failed the base check at the end of training, and needed a job fast. My previous employer, to whom I paid back the training balance AS AGREED, offered me my old job back, on either a temp or permanent basis.
In the end I joined another jet airline, completed the base check, and have enjoyed a good career since. But no way would that have happened had I scarpered from my first employer without paying my dues.
Anyone who suggests otherwise has no integrity. And the issue of airlines' integrity is irrelevant. I am ashamed to hear fellow professionals espouse such a dishonest course of action.