The Yellow Mountains were a range of mountains to the South-East of Middle-earth, a southern continuation of the Red Mountains. Both ranges were created when the Valar thrust the center of Middle-earth to the east as extra protection for Valinor.
Since it was a southern continuation of the red mountains the Dwarves of the red mountains could of moved south to these mountains and built cities and colonies. If it wassnt ever destroyed by the effects of the war of wrath.
We don't really know anything on the fate of the mountain range but it may have felt the effects of the War of Wrath and were ruined.