I use braid a lot and found that split-shot, ledger stops or rubber stops, just wont stay in place.
The simplest answer I have found, is using the biggest split-shot I can get away with, open the shot, trap it against finger with the line, bring the line round the finger and over the shot again, close the shot tight and pull the line either side to bring the loop to the back of it. The shot will not move easily but it will slide off the line if it breaks. Obviously, on a two-hook rig you do this twice.
On braid this doesn't appear to cause damage to the line. Not sure if mono would suffer, but then you dont need it on mono anyway.