Sacrifice the Tail
A large group that has come under attack is often called a dragon, and by analogy the stones trailing off one side of the dragon are its tail. The opportunity to sacrifice the tail often comes after the attacker plays a dual-purpose move which threatens to cut off some stones but also aims to undermine the dragon's eye space.
If the defender simply judges that saving the tail would saddle him with a heavy group (or worse, a dead one), sacrificing the tail is an example of an exchange. If sacrificing the tail provides the defender with a number of forcing moves against the attacker's cutting stones that help settle the defender's group, then sacrificing can be thought of as a tesuji.
This example comes from problem 209 of Weiqi Rapid Drill 800 Problems. is an incorrect way to kill.