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1.
To have rough sex, in such a way that it would be possible to break a condom. However it does not require an actual condom. The term can also be used for any harsh or semi-violent activity, such as a hard hit in football. The term originated from the song "Gangnam Style" because the chorus sounds like the phrase, "Hey Baby! Lets do it broken condom style."

Broken Condom Style can also mean to knowingly deceive a woman during sexual intercourse by using a ripped or defective condom.
He's going after her all Broken Condom Style.
by IAMAMERICANBADASS August 10, 2012
 
2.
The have very aggressive sex. Also is sometimes used for any act which is done aggressively or carelessly.
Wow, that's loud! Yeah, the neighbors must be doing it broken condom style again.
by HeybuddyKilledMe August 09, 2012