Interesting question, and one that I imagine depends on the vigilance of the bankruptcy court. It's hard to imagine them bothering to take away things like frequent flyer miles. I googled it and found this:
http://blog.zucklaw.com/blog/persona...ruptcy-indiana
Relevant portion:
Now, what about the status of an individual's frequent flyer miles when he or she files personal bankruptcy? As a board certified consumer bankruptcy specialist who helped write the exemptions portion of Indiana bankruptcy law, I want to begin by assuring readers that most people who file bankruptcy don't lose any of their property. In general, frequent flyer miles may be used only by the individual named on the account. That means that, although the miles represent an asset, they cannot be used to pay creditors towards the debts you owe.
However, certain frequent flyer programs allow the owner to redeem points towards a discount on merchandise purchased from participating online retailers. In this case, the trustee could take the vouchers and sell them to someone else, if the contract with the airline allows this.
One of the reasons I thought this reader question about frequent flyer miles was important is that it allows me to clear up a common misconception of bankruptcy as a punishment for people who have mismanaged their financial affairs. The old concept of punishment, complete with debtors' prisons, disappeared more than two hundred years ago. The modern image of bankruptcy is a safety net, designed for helping responsible people who have faced insurmountable obstacles rebuild their financial lives.
So, it looks like losing them is a possibility, but not very likely.