Not vector but physics really. You seem to understand vectors just fine, it's just that if an object doesn't generate any friction it will never stop. Well here we go:

PHP Code:
// enterframe function 
function onFrame(e:Event):void 

    
movement.+= 0.8
     
    
ballDist.bigBall.smallBall.x
    
ballDist.bigBall.smallBall.y
     
    
// if the smaller ball is outside the bigger ball 
    // perform reaction 
    
if(ballDist.len+smallBall.width/bigBall.width 2
    {     
        (....)
        
//Friction is applied
        
movement.*= 0.5;
        
movement.*= 0.5
         
        
/*if(movement.len < 0.4) //This is still quite a big number. I'd go with a value like < 0.000001
        { 
            movement.x = 0; 
            movement.y = 0; 
        }*/ 
    
} else {
         
//Friction is applied
         
movement.*= 0.95;
         
movement.*= 0.95
    }
    
smallBall.x+=movement.x
    
smallBall.y+=movement.y

Unless the ball is in a vacuum, it generates friction by rubbing against the air or whatever gas it is in. This is considerably less friction then rubbing against a solid wall, but friction none the less.