if the cross section curve is open then there is no way of capping it without making a volume out the surface first. that you should understand in the design process what you want to do and would be difficult to distinguish for others without an image or best as wim says post a file.
but if you mean that your object has a closed curve along the sweep but does not close at the ends which does not matter then, than if the openings are planar they should cap if not you had none planar cross section curves.
so if they are not planar and due to any reason you cant or dont want to change the surface you can use DupEdge on the openings that dont cap, split the curve with option points at two or more spots depending on the complexity and maybe you need some attempts to find the best places and use EdgeSrf then join.
if you necessarily need planar caps then you either use a CutPlane very close to the edge and trim a little peace off then cap. or you use SetPt for all the surface points at the ending, for this you may have to use orient to get the opening aligned to any xyz direction.