Some battles are as old as lawn maintenance it’s self…Weed Eaters vs Fences! I wish I could say there was an easy way to deal with this but there is not. Regardless of how careful you are, when it comes to trimming against fences there is going to be some line damage to the wood. There are a few “unsightly” alternatives but Im not in love with any of them.  We have seen people use brick pavers to line the fence.  This could get costly and also can look pretty random.  Some people even will use the metal edging for outlining your landscape beds against the fence.  Again, not very sightly.  The one that seems to make the most sense would be attaching a extra piece of wood to the base of the fence.  There is still going to be some damage to even this piece however the thicker wood will last much longer than the thiner fence boards.  Ultimately, unless you have small animals that will escape, have the fence stop just short of the ground is the best answer to fixing this problem in our opinion.  Hope all this helps!