I wouldn't be so sure that it would result in a liquidation. Perhaps a sale of the company and lease agreement between AMR and the 'sold' Eagle would be the most likely scenario. Many Major airlines lease aircraft to regional carriers that provide feed for them.
Companies divest (sell) businesses they own all the time, most of the time, it doesn't mean the assets will be liquidated.
Addressing the flight bennies, maybe if Eagle gets sold and planes leased back, you guys will have your AMR bennies for 5 years until something else is negotiated?... Although, when I was furloughed, I got to keep my DL bennies for 5 years. Hard to say what could happen.