You have to be more specific about what the actual requirements are, what your shape looks like etc. Naturally the first thing that springs to mind would be a particle trail that fades, but perhaps there are other things that could be used.
The easiest way I can think of to do this would be to start by drawing a shape layer with only a stroked path using the pen tool, press the U key twice to reveal the modified properties of the path, set a keyframe for the Shape 1 > Path 1 and copy it. Add trim paths to shape 1 and then animate the start and end points of the path.
The second step is to create another shape layer with a radial gradient fill by double clicking the rectangle or the ellipse tool. Then edit the gradient so the start point is at 0, 0 and is any color but fully opaque and the end color is any color but 100% transparent and, if you want the fade to be 200 pixels set the end point to 0, 200. Now press Alt/Option + p to set a keyframe for position and paste. Your gradient layer should follow the exact path of the stroke.
All you have to do now is set the top shape layer with the gradient fill as an inverted alpha track matte for the path and adjust the timing of the move to match the timing of the animated path.
As long as your path does not cross itself or have corners that are too sharp this should work just fine.
Here's a project file: Dropbox - TrimPath with faded tail.aep (note: your browser will probably add a .txt extension to the AEP file. Just remove it and you should be fine.)
Ah that's pretty much exactly what I was after thanks Rick!