Sanchez was the signal-caller for the Jets when they went to consecutive AFC Championship Games after the 2009 and 2010 regular seasons. You hate to boil anyone's career down to a single play, but Sanchez will likely be remembered by football fans for all eternity thanks to the infamous "Butt Fumble" instead of his body of work.
Here are his career stats. Note that Sanchez missed the entire 2013 regular season with a shoulder injury (and subsequently had surgery) after Rex Ryan decided Sanchez should play in the fourth quarter of the Jets' third preseason game back in August.
While the thought of Mark Sanchez starting games at QB for the 2014 Houston Texans is not the stuff dreams are made of, there's no evidence that the Texans are interested in bringing Sanchez in to start. Furthermore, there's no real evidence (yet, anyway) the Texans have an interest in Sanchez in any capacity; Rapoport's tweet merely suggests that he "expects" the Texans to have interest. That's little more than speculation, and it could be as simple as a reporter theorizing that the Texans will be interested in any veteran QB with a pulse.
Nevertheless, I ask you, BRB: Would you support the Texans signing Mark Sanchez? Even if it was purely to serve as the backup QB to someone else?