The term trajeck is used to refer to the overly traumatic past of a Mary Sue. It is related to "tragic" in the same way that "speshul" is related to "special," in that someone with a trajeck past has a past so traumatic that it gets irritating.
Trajeck Sues often have the same trademarks: abusive family, dead family, dead girlfriend, ran away from home, the works. Except that it is not actually tragic, since it often gets used as nothing more than a cheap plot device to attempt to gain the reader's sympathy without working for it and for the author to go "There, something bad happened in their past. Now I don't need to make anything bad happen to them again!".
Expect a Sue with a trajeck past to either ignore the "trauma" completely or engage in copious amounts of wangst.
Having a trajeck past is a charge.