I have found that the best way to handle calluses ripping off is prevention. Once one rips off, it is often painful to climb on even if you tape it properly. If you do need to tape, wrap tightly with a narrow piece of tape around the finger and make sure the loose ends are on the back of your finger.
For prevention, before climbing, check the skin on your hands for rough edges and small flaps of dead skin that are likely to rip off. You can use nail clippers to remove the flaps; cuticle cutters are better as it is easier to avoid cutting off healthy skin.
After you remove any flaps, sand any rough areas until they are smooth. You can use a nail file, sandpaper or a nail drill (i.e. an electric nail file made for use in cosmetics) for this.
It is important not to sand more than necessary as your calluses serve as padding for the structures inside your hands. This is especially true on overhanging jugs. I have gotten sore hands that forced me to take a few days off before from excessive sanding.