Marquis string suppressor ?
 

The rubber piece fell out, I put it back but it is just falling apart. Can I replace it with a different type.

RE: Marquis string suppressor ?
 

Glue it in with Superglue. And have your local Bowtech/Diamond dealer get you a half-dozen or so spares.

Make sure your string is properly centered on the string, and that you've got a slight gap between the string and the ShortStop ("slight" = I used a business card as the thickness gauge.)

It should last for at least 300 shots before requiring replacement.