I saw for myself and later heard about to instances when things went wrong on stage. In one of them a character was tied to a (prop) tree and was to be taken to the sheriff while the captors were talking on the other side of the stage. Unfortunately, the ropes fell off.

It's kinda hard to believe someone who only had to step over a few coils of rope lying on their feet wouldn't high tail it out of there but they picked up the rope and held it at waist level to (try to) preserve the scene.
The one I saw was the crucifixion at the church my girlfriend attended when the arm of one of the theves came loose, he had to work to keep up his part of the scene.
If you ever have to tie another active
to something, do it for real. OTOH, if someone's hands are tied behind their back and never shown to the audience, it's OK to just put the ends of the rope under their thumbs.
BTW, a faked tie up is part of the plot in the opera Carmen and her (new) boyfriend Don Jose gets into trouble for letting her get away.