If you are at the top of a drop and the person rappelling gets stuck while on rappel, the following self-rescue techniques can be helpful for lowering the stuck rappeller. Keep in mind that the easiest way to lower a stuck rappeller is to rig using a contingency method that allows you to quickly lower the rappeller without re-rigging. However, if the rappel was not rigged with contingency, you can convert the rigging after the fact if you have the proper gear and skills.
Reasons rappellers might get stuck on rappel include:
The last person down cannot be rescued using these techniques.
These techniques involve re-rigging while a person is weighting the rope and do not typically have redundency. A gear failure (e.g. a slide-and-grip knot that doesn't grip) during transition would likely lead to the rappeller falling.
These techniques can take several minutes, which can be critical if the stuck rappeller is under duress.