Green’s Dictionary of Slang

1. one who is to be hanged.

1562

Jacke Juggler Eii: You haue cause now to thanke this same hange-uppe For had not he bine you had faryd very well.

2. (US prison) a suicide who kills themselves by hanging.

1974		N.Y. Times 17 Feb. 14: Inside the Tombs a suicide is called a ‘hang-up.’.
1979		E. Torres After Hours 58: The hang-ups in the joint do it [i.e. hang themselves] all the time, even without a rope. I see a guy do it with his shirt. They bend their knees when they jump.
2005		N.Y. Times 28 Feb. B6/1: Suicides -- ‘hang-ups’ in the cold vernacular of the cell block -- have always been a jailhouse reality.