I can make a rope out of paper rather easily that is strong enough. The problem is it could not be completed in the time between guard checks, so a guard paying attention should notice the bedsheet is a lot smaller than it should be if he glanced in during the twisting process. Once the first stage is twisted it has to be doubled and twisted again, and during that time the guard could tell the sheet was missing. Maybe he could be fooled if the still untwisted part was spread out to give the impression the rest was under the sleeper, but not in the double twist stage. If the guards had been doing the bed checks at the right frequency, he probably could not have pulled it off, but it is possible to do all the twisting in under 15 minutes and a guard simply not notice the sheet was missing. If the guards skipped a round it is definitely possible to make a rope and asphyxiate in under 30 min. If they skipped two rounds, even easier.
The guard was likely asleep at their desk all night.