If you're asking which (American) airline is most financially stable, that would probably be Southwest.
Most of the others are losing money to some degree, with United currently under protection from Chapter 11 and American reportedly considering it.
The FF programs of some dead airlines survived -- Qualiflyer survived Sabena and Swissair, OnePass survived the demise of Eastern. Pan Am's flyers had their mileage transferred in Delta's program, TWA to American.