Negative infinity has an existence implied by infinity, as its negative. Negative infinity is not the additive inverse of positive infinity, because their sum does not equal zero.
Although negative numbers were not accepted by mathematicians until the 1600s, negative infinity is logically implied by the existence of Hell as described frequently in the Gospels. Also, the existence of an infinitely good God implies the existence of an infinitely bad evil that rejects God.
Negative infinity is difficult to define with independent terminology. Taking a cue from negative infinity as a representation of Hell, negative infinity is the lowest value possible.