Re: hanging tape off the ceiling
The sand texture will make things a bit more difficult to get a nice smooth finish, however, repairing your problem would be done the same as any other drywall tape joint. The loose tape is removed, new drywall compound applied, new tape applied, compound smoothed and built up as necessary to meet the surrounding area. dry compound can be feathered out with light sanding before new texture is applied. Be sure to spot prime and paint the patch first, then repaint the entire ceiling to blend together, otherwise you'll end up with shadows over the repaired areas.
Whether there is one coat or the standard 3 coats of compound on the tape, joint failure as you describe is usually due to improper installation to begin with, the fact that the previous owner only used one coat to set the tape isn't a determining factor in it's failure. More than likely, it failed because either not enough compound was used to set/seal the tape, air pockets remained behind after setting, or too much compound was removed from under the tape to maintain a good bond.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!