Final answer:
The ulnar nerve runs through Guyon's canal and innervates part of the thenar eminence and the medial 1/2 digit.
Step-by-step explanation:
The structure that runs through Guyon's canal and innervates part of the thenar eminence and the medial 1/2 digit is the ulnar nerve. The ulnar nerve is a branch of the brachial plexus and travels down the arm and forearm. It passes through the Guyon's canal, which is located at the wrist. From there, it continues into the hand and provides sensory and motor innervation to the hypothenar muscles, the ulnar side of the palm, and the medial 1/2 of the digit.