past tense and obsolete past participle of break (v.); extension to "insolvent" is first recorded 1716 (broken in this sense is attested from 1590s). Old English cognate broc meant, in addition to "that which breaks," "affliction, misery."
The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with go broke
Also,go bust. Undergo financial collapse, lose most or all of one's money. For example, The company's about to go broke, or The producer of that movie went bust. The first expression dates from the mid-1600s; the second, slangier variant dates from the mid-1800s.