past tense and obsolete pp. of break (variant of broken); extension to "insolvent" is first recorded 1716 (broken, in this sense, is attested from 1590s). By coincidence, O.E. cognate broc meant, in addition to "that which breaks," "affliction, misery;" but that sense died out long before the current one began.
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
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.