Parallel

"'The Parallel is a dark reflection or echo of our world. It is a place of decay and death, a plane out of phase, a place with monsters.' -Dave, when reading the D&M instruction manually."

The Parallel is the YEZ equivalent to the Upside-Down. It is first noted that Claws lived here before his discovery of Yoshi Suburbs.

Where Is It in Yoshi's World?
"'It is right next to you and you don't even see it.'- Dave, reading from the D&M manual."

The Parallel is directly below the universe! Upside-down, of course, it was almost called the Nether, the Topsy-Turvy, the Upside-Down, or the Other Side, blankly.

Residents
Some of the residents (none has ever stayed) were briefly Medium Gil, Krystal, Claws, Eyes, Speako, Two-Face, Two-Face, Jr., Bomber and Bomber, Jr., Clawbot, JUMPOFF, and Shadow Titan while still Shadow Kirby.