In my short tiger barb experience, there seem to be at least three versions of this behavior worth distinguishing between:
Sleeping/45 degree it seems to me that the tiger barbs sleep in a more or less stationary position, inclined downward at a 45 degree angle. This position is very relaxed looking, and they usually concealed near plants or the bottom. Color is often faded while sleeping, then returns shortly after waking.
Straight down - extended duration: straight down position, seeming to struggle to stay in place as though over buoyant. This behavior seems to be related to stress ... and it's kind of stressful to watch, too. If conditions are not improved secondary diseases and death can follow in time, it seems. Water changes may provide short-term help.
My new barbs were doing this until I discovered my pH was high (over 7.8) - I did a 20% water change and removed two limestone rocks that were raising pH, and the Barbs stopped immediately and have never done it since. A friend had barbs who did this continually, and almost all died within a couple of weeks.
This behavior might have something to do with swim bladder, or perhaps this position and swimming motion may help with digestive problems brought on by stress? Either way, continued vertical position swimming seems to be correlated with tiger barb stress or illness. Check water parameters and watch closely for disease.
The "Faint" : An active barb occasionally goes nose down, fins are all erect, color faded. Slowly, slowly glides downward an inch or more. Slight fin fluttering. Seems to occur only in presence of other barbs, but this might be because barbs are hardly ever alone. Can snap out of it and behave normally seemingly at will. Might be some sort of display, or who knows ... maybe they're just farting. I have not seen any correlation between this and sickness, but we'll see. Has anyone else seen this happen? Maybe something weird is afoot in my tank ... or maybe this is because my tank is cycling.
Anyway, I'm no pro but I do watch my barbs a lot ...