factions, what happens when you leave

When you leave a guild, does the faction drop of that guild drop somewhat, or stay the same?

It stays the same. Once donated, faction stays with the guild until it goes away from faction decay.

although, a guild leaving an alliance does subtract from the total alliance faction

No the faction does not drop but a guild leaving a alliance the faction that the guild has to its name is subtracted from the alliance faction which is the totaled faction of all the guilds in the alliance..

If a player leaves a guild no faction is removed. Just watch out for them stealing the copperwire out of the Guild hall

Keep in mind that the guild's total faction is based on what each player has donated to the guild, not how much that player has in his title/faction counter. Players do not "store" the faction after they donate it.