If the finish is peeling off the first ten feet of line, don't cut the line! First, light a match and burn the end of the exposed line. If a hard ball of resin forms, you have a Nylon line that is not worth bothering with. If there is only ash, it is a silk line and you may be able to save it.
Personally, once you cast a good silk line, it is hard to go back to PVC for dry flies and quiet water.
Here is something I wrote years ago about silk lines for American Angler - Over My Waders. I still believe it holds true.