I always got the impression that this was standard practice in most clans, but those it is specifically called out in make more or better use of it. I figure most of it goes something along the lines of
1) Trial of position for a combat cluster position
2) Trial of position for non-combat cluster position (guard duty, police, etc. - potentially even PBI in a combat cluster)
3) Trial of position for a civilian position
4) You are a failure, become a laborer
Any of the first two could, and probably often do, result in the death of the potential warrior. Those clans which are specifically called out to allow for secondary trials are for other combat cluster positions, a MW or ASF pilot could become a battle armored warrior, or a tanker could become tanker crew, etc.
I don't have any fluff to back any of this up, but this is kind of how I see the clans working.