There are a number of synonyms for the phrase "give one the slip." One might say that they "evaded" or "eluded" their pursuer. They may have "escaped" or "dodged" their tracker's grasp. Another way of saying this is that one "shook" or "ditched" their follower, or perhaps they "lost" them in a crowd or in a maze of streets. Regardless of the terminology used, the meaning remains the same; someone has managed to avoid being caught or tracked down by someone else. It may be because they possess superior skills at evasion, or because the person pursuing them was not skilled enough to keep up with them.