Often used to describe someone physically preventing another's hard fall. When she stumbled on the ice, he quickly moved to break her fall.
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Metaphorical Use
Can describe reducing the impact of a metaphorical 'fall' such as a failure or loss. The community fund was set up to break people's fall during tough economic times.
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Emotional Aspect
Sometimes used to express care or empathy by lessening emotional hurt. After the bad news, her friends gathered around to break her fall.