Non-existent space is a dimensional void between the Nameless Zone and the Land Beyond. Beneath the Dimension Bridge is a layer of fog, beneath which is absolute nothingness. Anything or anyone that falls beneath the fog will forever cease to exist. The Dark Orb was thrown over the bridge by Tails and ceased to be, and The Dark One was destroyed with it. Trogg almost fell towards it on two occasions, but managed to hold on to it a rope each time.
Early strips didn't mention the non-existent space's properties. Anyone who fell off of the Dimension Bridge was merely suggested to be heading for a fatal fall into the chasm below. It wasn't until The Revenge of Trogg where the void came into play, conveniently in time to get rid of the Dark Orb. In Sonic the Comic Online, a goblin immigration officer suggests the space is the reason why people rarely travelled along the Dimension Bridge, despite there being a spell protecting the Nameless Zone at one point and the barren landscape of the Land Beyond not proving to be a popular holiday destination.