Explanation:

Spaceify goes down in the basement to throw out all the trash in there because he lost to everyone else in a well-played game of poker.

when he goes down there, he finds a TV, thas jill. ( I was thinkin' jill has the power to hide her body and act as an actual TV )

Jill is alive and is a square head, when space introduced jill to everyone, everyone agreed she too can be a square head

fin

Headcanon: Jill was made by an engineer ( from tf2 :flushed: ) as a moving TV, so the engineer can watch TV anywhere.