JavaScript (ES6), 25 bytes

s=>/(.+?)\1*$/.exec(s)[1]

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Regular expression

   +-------> 1st (and only) capturing group: 1 or more character(s), non greedily
   |   +---> reference to the capturing group, repeated 0 to N times
  _|_  | +-> end of string
 /   \/ \|
/(.+?)\1*$/