Ok here is what you need to do. Add an object like a null and name it Transparency null. Place it at the end of the rope where you want it to burn. Now when you make your transparenct gradient use the "? distance to object". So if your rope is perpendicular to the y axis you would choose "Y distance to object" and set the transparency null as target object. Now make your gradient so the transparency extends below the null away from the rope but the transparency should start right at the null. Now just animate the null moveing along the rope and poof it disappears right at the null.
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