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1.
(N) An accidental crossfire during a sexual encounter with a woman involving two or more men, generally referred to as a "gangbang." A man aims his penis in error at the moment of orgasm, offloading onto another of the male parties involved. The Texas Surprise is generally most potent when the cumshot winds up on the face of the receiving male.
"After pulling out to finish, John was so enveloped in the heat of his orgasm that he didn't realize he'd given Tim a Texas Surprise!"

"Dude; that guy just gave Ron Jeremy a Texas Surprise! He'll never get work in this town again!"
by Auralius June 05, 2013
 
2.
Taking a big dump in a toilet without flushing and leaving it for someone else to find.
I left a texas surprise for Dr. Ikpatt in his personal bathroom, he will never know it was me!
by Plausible Deniability September 27, 2014