I have had loads of flexibility on cheapo inflexible tickets over the years with airlines as diverse as BA, SAS, Czech Air, Air China and many dodgy Latin American airlines who's names I can no longer remember. Generally the airlines allow some flexibility in the system and its a case of simply finding the right person.

Recently on one airline I turned up a day late by accident on a VERY cheap ticket and they still flew me!! (they were very angry though!)