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Someone who easily gets drunk. They could have 3 shots of a 40% strength alcohol and they're gone. The person is cheap because they don't have to spend as much money on alcohol to get drunk.
See that midget over there. I bet he's a cheap drunk
by Catch Phrase July 13, 2006
When somebody has a few drinks at a party and ends up in the back room having sex with random guys.
I can't believe Sisi is in the back room on a crate waiting to have sex with a group of guys

That's nasty Jerry! Sisi is a cheap drunk!
by Friday13 August 04, 2010