I'm kind of perplexed on this one, because you could be talking about one of two things.
Either you're trying to make a "clothes line" (which sounds an awful lot like 'close line' : ) or you're trying to make a "closed line"...
I think it's the latter because you discuss merging points in polygons, so I guess you meaning merging verts to "close them".
As far as making a closed line do you mean a closed curve line i.e. in NURBS modeling? This is a shot in the dark but if that's what you're trying to do then you can hold "X" while you construct the curve to snap to a grid. That way you can snap the first point of the line onto a grid, draw whatever else you want, then make sure you snap the final CV point to same grid position as the first point to "close the line".
So tell me...was I even close to answering your question? : )
-FS_RAZ
