"Solitaire ending " effect using Echo effect

Start by pre-composing the moving layer you want to echo, name the layer Echo, make sure that you Move All Attributes to the new comp, and Open the comp. Pre-compose again, moving all attributes and naming the new comp Original, but do not open the second copy. 

Apply Echo to the Echo comp, move to the last frame and this expression to echo time: 

- thisComp.frameDuration

 Now set the Echo Operator to In Front and start increasing the number of echoes until you get about the number of echoes that you want in your final comp. Don't worry about the starting point yet. 

Here comes the fun part. Open the composition settings using Ctrl/Cmnd + K, go to the Advanced tab and select Preserve Frame Rate when nested, return to the first tab, and start fiddling with the frame rate until you get the echoed frames to cover the motion path completely. The Comp Preview will update if you click off the frame rate. When you have the echoes starting at the initial position of the moving object, close the comp.

Check the work. In this example, the frame rate was set to 12 fps. 

Because the frame rate of the nested comp matches the frame duration of the echo, the moving object will not move in the frame. You should now be able to return to the Main comp and have the laying down Solitaire effect.