I think you mean a "tank slap," ie when the handlebars wobble back and forth uncontrollably... ?
If u ride on the street, it's not very common, but it -can happen- depending on road conditions and speeds.
Best way to avoid it is to (a) don't go over any bumpy patches of road and keep the speeds in check, or (b) install a steering dampener.
GPR makes a very affordable one for the FZ6R. I have the GPR v4 on my R6, which I picked up in a group buy off the R6 forum from www.cyclesector.com in San Diego, CA. Was $350 + tax & s/h. And, I love it. I can run over pot holes and squirrels now without skipping a heartbeat.
I posted the same problem on here recently (although, don't know where). Turned out I had a small piece of newly paved asphalt stuck in a tread, creating an uneven crown on the tire, combined with a slightly bumpy road, and voila... tank slapper...