Broken halyard lasso
Trevor Ventham recovers a snapped halyard without climbing the mast
If a halyard snaps and there’s someone prepared to climb the mast safely, retrieval is not too much of an issue. For the rest of us, perhaps this device might help.
Fix one end of a wire loop to a snap shackle eye and the other end to a control line threaded through the eye. Attach the shackle to a spare halyard and add another control line to the shackle so you can guide the entire contraption to the location in mid-air (probably downwind of the masthead) and lasso the errant halyard with the wire loop.
The less wind, the easier it will be, though mast and hull movement is also bound to be unhelpful!