That is a rear cinch, that helps to stabilizer the rear of the saddle, especially when moving quickly and turning, etc. There is also a connector strap that runs between both the front and rear cinches, and if it is not used it can cause a very bad reaction from the horse should the rear cinch slip back.
In that picture, the rear cinch is not properly adjusted. It should not be tight like the front cinch, but should be snug so the horse cannot get a foot caught in it. It also needs to be snug, or it defeats the purpose of it being used. There is a connector strap being used properly to keep the rear cinch from slipping back.
Could that contribute to an accident? Yes.
Please note I am just providing facts, not judgment.