Green’s Dictionary of Slang

abe n.

[Stephens & O’Brien, Materials for a Dict. of Aus. Slang (unpub. ms. 1900–10), suggest link to abraham-man n.]

[1900s–40s] (Aus. Und.) the last of anything; the only example.

In phrases

on one’s abe (adj.)

[1900s–40s] (Aus.) impoverished.