There is no straightforward answer to this question; in some cases, catching a falling person may help the faller avoid more serious injury, but thanks to something called deceleration trauma, the impact of a catch can be as physically harmful as an uninterrupted fall Some people say that it's not the fall that causes damage, but the landing, meaning that the physical impact of being stopped (landing or being caught) while in motion is much more harmful than actually being in motion (falling uninterrupted). However, there are real-life examples of people helping others by catching them as they fall.
For instance, in 2012, a man in New York City caught a 7-year-old girl after she fell out of a third-story window. According to a physical analysis of the event, this man's catch saved the girl from much more serious potential injury. The man, Stephen St. Bernard, did sustain a torn shoulder tendon as a result of the force of impact of this catch, and the little girl did suffer some minor injuries, but they both walked away from the event with their lives. The exact answer as to whether catching a falling person will save them may depend on the specific details of the situation, including how far and fast the person is falling and what materials are used to stop their fall.