The ideal time is JUST BEFORE it breaks.
We had a kevlar halyard break shortly after we purchased our boat.
It was only five years old, but had spent a year in Mexico
It was time to reef, so I winched the halyard just a bit to relieve the sheet stopper and BANG !
The halyard snapped between the winch
and the sheet stopper.
We would lose the halyard inside the mast if we opened the sheet stopper which of course, we didn't want to do under the circumstances.
thankfully moderated enough so we didn't have to immediately do anything, so we formulated a plan. DUCT TAPE to the rescue!
I spliced it with just enough to hopefully hold the two ends together, but not enough to prevent the line from sticking in the sheet stopper.
Talk about a balancing act! No second chances here...
When we sailed into the lee of the island, we opened up the sheet stopper and thankfully the halyard splice fed perfectly through, up the mast, down the 2:1 halyard.