Those in the same faction will not be able to loot each other. The exception to this is if they are in the same party, with looting rights turned on. As long as the deceased character does not receive any lawful damage his faction-mates in the party can loot him. For example, if a character is killed by a monster, a player outside of the faction wars, etc., his faction mates in the party will be able to loot him. Lawful Damage is defined as consensual combat from enemy guild members, enemy virtue guild members, and enemy faction members.
Lawful damage is also justified damage returned by a player against an unlawful aggressor.
If player A and Player B were in opposing guilds or factions, then player A's initial attack would be lawful damage. Only a player with looting rights will be able to open a corpse on Trammel. In Fellucca, players will only be able to cut up the corpses of murderers, or if the player is a murderer then they can cut up any corpse. Those lawfully damaged by the looter. Only the players who did lawful damage will be able to loot the corpse without going grey.