Each Life Support module allows a ship to have up to 4 crew aboard. Note that this is long term crew. During the Phases and Rounds of a mission, ignore this restriction. A single boarder showing up will not overstress your Life Support but if you were to capture them and bring them home, the ship's Life Support would get overstressed.
Life Support damage is subject to alien and special abilities but not armor.
If there are more characters aboard a ship for a leg of a long space voyage than it has sufficient Life Support, those aboard will suffer damage. For each character aboard the ship that exceeds its carry capacity, each character aboard suffers a die of damage. Thus, each of 6 characters aboard a ship with a capacity for 4 would suffer 2 dice of damage. This damage is luckable but cannot be healed until the end of the campaign turn.
Any character in space that is not aboard a starship or fighter must make an Athletics skill check of 11 at the end of each Phase or suffer 1 die of damage. This is not mitigated by armor but is subject to alien abilities.
If all Life Support modules are broken or slagged, all characters aboard must make a passive Athletics check of 11 or suffer 1 die of damage at the end of Phase 6.
A character with damage exceeding their hit points by 6 or more is dying. They will automatically suffer a die of unsupported Life Support damage at the end of each Round as if their ship's Life Support had failed, unless a successful CPR is performed on them (see page 34). If it is, they must make the Athletics check of 11 or suffer unsupported Life Support damage.