It is important to realize that pellet stability and slug stability are different forms of the same phenomenon.
Our typical Diabolo (waisted) pellets primarily get their stability from the Center of Pressure (CP), caused by the drag of the flared skirt, being behind the Center of Gravity (CG). This makes them naturally stable in flight much like the behavior of a dart, arrow or Badminton shuttlecock.
When the pellet is not travelling straight, there is more pressure or drag on one side than the other (left drawing), and the CP is offset, causing a torque or twisting moment about the CG.
The pellet will tend to yaw less until the CP is directly behind the CG (right drawing) and the pellet travels straight. This is called “Shuttlecock Stability” and pellets are often referred to as “Drag Stabilized”. This is not strictly true, pellets are “Flare Stabilized”, but the effect is the same.
Unfortunately, very few slugs are perfect. There may be tiny voids in the lead, or imperfections from casting or swaging, that causes them to be asymmetrical. This results in the CG being offset from the shape (and hence the CP), as in the upper right sketch.
In addition, as the forces realign, the slug yaws. There is also a reaction to that yaw which causes the slug to suddenly depart from the direction the barrel is pointing.