Each time a player dies, a record of his current alignment is made - his soul fragments. For example if a player has died (meaning actually died, not just downed - someone did a FINISHING BLOW) a total of 20 times, at the end of the era the game will roll 20 times what will be the new alignment with weights affected by the records of those deaths. The faction that has rolled the most times will be the new faction.
New vessel (newborn) for this player's soul will have it's alignment set to these values.
More on (new) vessels in families.