When Jeroboam leaves Jerusalem he met the prophet Ahijah:
And at that time, when Jeroboam went out of Jerusalem, the prophet Ahijah the Shilonite found him on the road. Now Ahijah had dressed himself in a new garment, and the two of them were alone in the open country. Then Ahijah laid hold of the new garment that was on him, and tore it into twelve pieces. And he said to Jeroboam, “Take for yourself ten pieces, for thus says the LORD, the God of Israel, ‘Behold, I am about to tear the kingdom from the hand of Solomon and will give you ten tribes (but he shall have one tribe, for the sake of my servant David and for the sake of Jerusalem, the city that I have chosen out of all the tribes of Israel)
(1 Kings 11:29-32 ESV)
Ahijah tears "his" robe into 12 pieces giving 10 to Jeroboam apparently as a symbolic action showing how the LORD will make Jeroboam king over 10 of the tribes of Israel. He also says one tribe will remain under the rule of the House David.
What did he do with the 12th piece and how should the symbolic act of tearing the robe into 12 pieces but only specifying the rule for 11 pieces be interpreted?