Poop hanging out of ... you know.

I've seen this happen often at the shelter, and usually we just take a damp tissue and remove it. Does it mean anything bad? My cat had this happen today, and he was traumatized (nothing strange) because he's skittish in nature and for some reason is afraid of tissue papers. I only noticed it because he was sitting funnily, so I checked closer and saw a piece sticking out. He wasn't vocalizing pain or anything, but then again, cats are really good at not doing that.

It wouldn't come out easily (as in the usual case where a quick wipe would do it), and I was so afraid of hurting him, but aside from being all wide-eyed (I had my roommate hold him), he didn't make a sound. I wasn't yanking the thing out his anus, but it wasn't an easy wipe either. The poop itself is nothing special, same color (light brown) and texture and hardness as the ones I scoop out every day. 5 minutes after I praised him for letting me handle him, he was back to his usual self. 

Is this constipation? Should I be keeping an eye out for anything?

I have had this happen too with some of my cats I have had over the years. I think that your cat should be fine, it is likely just uncomfortable for the cat to have it "stuck in there". I doubt you hurt him, and I bet he was relieved that you got it out too, if you are concerned about constipation, I would just keep an eye on it.

He is likely okay, just had a rough day in the litter box.

Could be hairball poo, very dence. Usually cats break sticking piece off by "gliding"/wiping their bottoms at the floor. A little bit of coconut oi or olive oil on Q-tip and oiling exit may or may not help. As a last resort, washing bottom at a sink, poo, after becoming water logged, dissolves or breaks. If cat allows washing, of course.