Better question - minor factions can be ousted from systems and in the end entirely quashed. What happens when you've paid a few thousand quid to get your minor faction and someone does that to it? Do bought player factions simply become invincible and undying, or are they as fragile and vulnerable as all other minor factions?
A tad off-topic, but so far I've
never seen a Faction being removed from a System due to being "stomped" in terms of Influence.
They'll still happily sit inside the System even at 1% or less forever for all I know.
Personally, I regard Player Factions just like NPC Factions which (by grace and approval of Frontier) were merely given a custom String and maybe a description in the System Map.
No means to limit/specify Bulletin Mission types they offer, no means to influence System Security, no means of control over what they do - thus they're still just like any other generic NPC Faction.
PS.
Although not the fault of the Player Groups themselves - their current core issue is being placed into Systems with already existing Player support and being handed the main Station and System control for free.
That instantly wipes all effort & work other active Players have invested... overnight. Talk about giving Players a surprising "crowbar to the face", because that's what it is.
Sad climax so far : Pleiades Station in Maia.
Everything one could possibly do wrong concerning placing Player Factions around... Frontier did. All mistakes at once.
A textbook example of
how not to do it and
how to abuse and (expletive)-off thousands of Players that invested weeks of hard work.