Green’s Dictionary of Slang

to the very end, until everything is resolved.

1860		Wyandot Pioneer (Uppr Sandusy, OH) 13 Sept. 2/2: We have made up our mind to stay with Warrne P. Noble [...] ‘until the last dog is hung’.
1880		A.W. Brown Can She Atone? 160: I‘ should think with such luck as you've had you would want to stay till the last dog is hung’.
1915		Princeton Alumni Wkly 15 688: About the Reunion he writes: ‘Am going to come early and stay till the last dog is hung’.
1922		Forum 67 535: Those wets [i.e. anti-prohibionists] who hang out till the last dog is hung are the ones who will cause the last dog to be hung.
1965		A. James America’s Homosexual Underground 139: They gotta hang around the bar until the last dog is hung.