I wrote about this once in a print magazine, and some people were skeptical. But I’m telling you–it really does work. I’ve done it twice at sea successfully; no fuss, no muss. If you lose a halyard up your mast, this is how to get it back from deck level without having to climb the mast.
There is one prerequisite. You need a spare halyard with a shackle on it that is in reasonably close proximity to the one you were stupid enough to let fly up the mast. Given this, retrieving the lost halyard should be easy.
Step 1: Take a loose length of line that is long enough to reach the lost halyard from the deck and tie a noose in it with a slip knot, so that you can pull the noose shut.
Step 2: Clip the noose line with noose open into the shackle at the end of your spare halyard, as shown in the detail drawing above. It need not be a snapshackle. (Note the relative size of the shackle and noose line in that drawing is all askew. The shackle will, or should, be small enough that the slip knot can’t pull through it.)
Step 3: Use the spare halyard to hoist the noose line aloft up close to where the lost halyard is.
Step 4: Now twiddle about with the noose line and spare halyard from down on deck until you succeed in lassoing the lost halyard. This is not as hard, or as unlikely, as it sounds. It helps a lot if your noose line is a bit stiff with salt and/or UV damage, as this helps the noose stay open. It may take some patience and persistence, but you should succeed eventually.
Step 5: Having lassoed the lost halyard, pull gently on the noose line until the noose closes around the lost halyard.
Step 6: Now pull the noose line down to the deck, and it will bring both the spare halyard and the lost halyard along with it.
If you don’t believe me, just try it while tied up to a dock or mooring.