(Courtesy of FanGraphs. Click to enlarge)
That graph shows Matt Thornton's career K/9 trends. As you can see, it's broken down by K/9 against right-handed and left-handed hitters and as you can see, both of those lines have been trending in the wrong direction for the last 3 seasons.
Part of what makes Thornton a bit of a risky signing is that major decrease in K rate he's experienced since 2010. The loss of swing-and-miss stuff has made him much more susceptible to getting tuned up by right-handed hitters and since 2010 that's exactly what's happened. In 2010 righties posted a .254 wOBA against him. In 2011 that increased to .291, in 2012 it was .302, and this past season it was .370.
Thornton is no longer the dynamic reliever he was against hitters from both sides of the plate. He's devolved into a lefty specialist only and there's reason to be concerned that his effectiveness against lefty hitters could start to deteriorate as well based on his downtrend in strikeouts. It hasn't happened yet (.280 wOBA vs. lefties in 2013), but it could. Righties have figured Thornton out now that he's not throwing the same smoke he used to. It's not out of the realm of possibility for lefties to start doing the same.