fray
To wear out and come apart at the edges.
Fray means to become worn and unraveled at the edges, like what happens to the cuffs of your favorite jeans after you've worn them constantly. The threads start to come loose and stick out in little strands. An old rope might fray until it becomes weak and breaks. A beloved stuffed animal's ears might fray after years of hugs.
The word also describes a fight or conflict. When someone enters the fray, they're jumping into a heated argument or battle. If a playground disagreement turns into a shouting match, you might decide to stay out of the fray rather than get involved.
Notice how the two meanings connect: both involve something coming apart or getting messy. Just as fabric unravels into individual threads, a peaceful situation can unravel into conflict. A teacher trying to break up a classroom argument might find her nerves frayed afterward, meaning she feels worn down and stressed. When tensions are high and people's patience is wearing thin, we say tempers are fraying, like a rope about to snap.