well leyla-sama was rescued from the ship which volk and some other from the original dozen destroyed by cross, he taught her the martial arts as well and made her endure all the hardships during the training by impersonating volk whom layla hated and wanted to kill, probably cross used a shuttle to rescue her --> cross later sacrificed himself to show layla that revenge would bring her no satisfaction
volks idea was to sacrifice most of the martians and let some (1 city of that fighter who won) survive and later as nei seems to be capable of giving birth recreate the human race again --> humans on earth are destroyed, though i dont remember what his plan was to survive the impact of the moon (its the moon from earth i guess, so earth is completely destroyed and the moon was travelling through the solar system until it reached the grav field of mars (mars has no own moons), well anyway seeing it realistic the humanity is doomed as the plan failed with volks death and after a moon crashes into a planet there will be not much left, but maybe it wanst that the moons should crash but only enter the grav field and.... woooh i actually missed the topic again
so the ending again: it was sort of a breakdown of the society created by the original dozen, all that representative fighting rationalisation of ressources to winners and letting the winners be saved from destruction etc, the next step would result in anarchy
layla could have brought order into this system by staying and taking the lead but she didnt ... -> so anarchy would definitely result and as anarchy cannot exist for long due to its nature the people of mars would now form a new society, but as i said, i somehow missed the part in the anime where it was said how they actually wanted to survive the cataclysm... argh and this is making me so nuts!!!!!!!!!!!!!!! im not getting the complete picture!!!!!!!!!!!!!