BobDDuck
Island Bus Driver
In the picture there is more lift generated on the right wing due to prop wash, and more drag on the left due to the dead prop.
To counter side slip toward the dead engine the left wing is raised (raise the dead).
You can see how the the airplane is now at high drag/low power.
In other words you have a lot of forces pulling/rolling to the left so its imperative to keep the rudder effective =maintain speed above VMC.
Others will hopefully chime in on that important issue.
Pretty much except for the highlighted bit. The contributing effect an operated engine has is related to the yawing motion generated by a force (the engine) acting via an arm (the distance from the CG to the engine).