The term falling knife (also known as "Catching a Falling Knife" or "Catching the Bottoms") refers to the action of buying an asset which is rapidly declining in price.

Such an act is usually supported by the assumption that one could predict the bottom of the declining price right before a Dead Cat Bounce or a price reversal occurs. If a trader successfully “catch the knife,” buying the asset very close to its recent bottom, they would make a good profit on the way up.
However, trying to catch a falling knife is undoubtedly a very dangerous endeavor and, in reality, most knife-catching attempts fail and often result in significant losses.

Examples
When the dot com bubble started to burst in 2000, and the prices declined 50-60%, many traders started to “grab good deals” and buy shares of Internet companies, anticipating a sharp reverse and huge gains. A few weeks later the bubble popped completely, and most of the alleged “good deals” became worthless.

In December 2017 Bitcoin sharply dropped from $20,000 to $17,000 and many people saw it as a chance to get in and started buying in anticipation of potentially new highs. A few days later the price landed at $10,000 level, marking a -35% from what had been initially considered as a “good deal.”

These are two primary examples of knife-catching failed attempts, which certainly caused big financial losses to many traders and investors worldwide.