I usually use a CoordinateExtractor (with index 0 and -1) to get the first and last coordinates of the line.With a VertexCreator (replace with point) I create new points for these lines.Next I use a NeighborFinder to find the closest to points and use another VertexCreator (add vertex) to create the lines to close these openings.

Could you intersect your problematic lines against a line corresponding to the sheet limits?(if not available,the accumulated bounding box of the data might work).Then just keep the pieces of the sheet that are connected to data at both ends.