In Dark City, everybody seems to have memories of Shell Beach planted by Strangers which doesn't even exist. It also gave the main character a reason for searching it. But why did the Strangers imprint the memory of Shell Beach when they were not even supposed to remember where it exists? Why did the Strangers make this memory loophole?
The people of Dark City are kept in the city in darkness. Part of the way the Strangers keep the human populous from suspecting they are part of an experiment is to keep them from realizing that fact. So, they implant them with memories of being outside the city, in the daylight, to keep them docile. Shell Beach, in particular, represents hope. Without the belief that there is something better just outside the city, the humans would likely go mad with the realization that they are stuck in an elaborate prison. Of course, since there is no actual Shell Beach, they keep the memories vague, so that everyone thinks they know where it is, but can't give clear directions. Nobody questions this because they've all been programmed by the Strangers not to -- until John Murdock comes along.
John Murdock knows there's something wrong with the city, and his partial memory implant gives him glimpses of Shell Beach, which he latches onto as a means of unraveling the mysteries of the city. John lacks the programming to accept things as they are, and his questions eventually lead Bumstead, who has been programmed to be a detective, to join him. He is, in essence, looking for hope, and in the end, he must create it himself.