Can't tell you about Delta, but I know for a fact that AA does it. I've read about it on AA forum some time ago, so I decided to test it. I was about 400 miles short for a 50K award, so I signed in to my account and went through the motions of claiming the award just to see if it would go through. It did . I did not finilize the award as this was just an experiment, but I assume it would finish if I chose to do it, because I also tried a 60K award, and it stopped me cold as soon as I asked for it.