I have not heard of anyone waiting to pass phase II before taking a class date. I also have not heard of anyone passing phase II until typically just days before finishing IOE. I am not sure why but I have a feeling they wait to extend the "full" offer for some reason. A few folks I know waited a few months for a class date and knew for a fact that their background checks were done and they still got notice of passing phase II just a few days before completing IOE.

Not sure how it works but I have no idea how long you would be waiting if you waited to officially pass phase II before accepting an offer.

If it helps at all, most people are likely in your shoes (maybe minus the baby.) Most folks are currently employed with 5-15 years of seniority where they are and in the left seat and they choose to leave that on a conditional offer. I would *think* that they would not offer you a class date if they were not comfortable with you as a candidate. I would say the only fear would be an actual problem. If you did not disclose something such as a criminal offense or a failure or violation, something along those lines. I just dont see them sending you to class and then potentially a few weeks short of completion or even in IOE sending you a fedex package giving you the "thanks but no thanks."

edit- As for the out of business employer...no big deal. The company that is subcontracted to do background checks will get a hold of you and you will work it out with them, not jetBlue. They are very used to that sort of situation in aviation and they will tell you what you need to do to tie up that loose end.