Does it appear that there are fibers protruding from the concrete or is it literally just breaking down and really powdery? If it is just flat out breaking down and becoming powdery you need to etch the concrete with muriatic acid to stop the efflorescence. If you can stop the efflorescence your best bet would be to get a moisture cured urethane and coat the floor, but only if you can stop the efflorescence, otherwise the urethane will fail. Pictures would help.