There have been ample instances of that over the last six years. Two examples I recall are the DC snipers doing freelance jihad, and the Egyptian national who shot up the El Al counter at LAX. But in the meantime, let's just open our borders and let everyone in!
Check the stories under the keyword suddenjihadsyndrome:
http://www.freerepublic.com/focus/keyword?k=suddenjihadsyndrome
Perhaps not all these stories can be explained that way. But when you apply Occam’s Razor, it’s the most likely explanation, for many of them.