A cloud break procedure is usually used where there is not a published standard instrument procedure to a specific airport.
It was used years ago, together with a canyon approach (rapid descent and pull-up) to access those airfields with high terrain around.
KASE (for example) had one years ago before the VORDME or GPS procedures were established.
If you look at the VORDME approach to ASE now, it is essentially a cloud break procedure with minimums of 2380ft/3sm.
Same for KEGE with LOC -B minimums of 3625ft/3sm.
These airfields require a good degree of caution.