I'm not sure how in-depth you understand the Power Play mechanic, but here:
Zac Antonaci said:
Will Minor Factions/ Powers have alternate methods of expansion than the current Top 10 Powers? Say, Anarchists spreading through cop-killing, Democrats via elections, etc.
The mechanisms will be the same as the current powers.
This to me doesn't suggest a change to the undermining mechanic. Rather it suggests that the undermining mechanic is going to stay exactly the same as it is now.
In addition, the mechanisms in place for undermining a minor faction are very different to those in place for undermining a Power. In the case of the former, undermining a minor faction is enacted by bolstering the influence of the other local minor factions at a cost to the influence of the targeted minor faction, usually through the auspices of a bulletin board mission, or more directly by choosing the opposing side in a CZ (if one exists).
For now, player minor factions are going to be just that, minor factions. When and if they become Powers will be determined at a later date, and as yet I've not seen anything from the Community Team or the Devs to suggest what mechanism will be in place to allow for minor factions to be upgraded to Powers (though obviously, if someone else has that information it would be appreciated).
Within the context of this thread, Dave1235's suggestion basically relies on CMDRs undertaking missions for any and all factions other than the Code's minor faction in their home system, effectively raising the other factions' influence and thereby reducing the Code's. This sort of pseudo-guerilla warfare can be just as effectively achieved in Open, Group or Solo modes with little or no chance of opposition other than Code going out of their way to do every single mission they can find posted to the bulletin boards in support of their own minor faction.
(Just as an aside, I may be wrong but if IIRC then accepting a mission and then abandoning it uncompleted also reduces the minor faction's influence - I'm not in game right now so can't check - if anyone else is willing and able to check this then clarification would be appreciated).
With regards to eradicating a minor faction completely, I'm not sure if this is actually possible, and even if it is there's no guarantee that it will work against a player minor faction, given that these will be minor factions effectively created by the player base - I'd hope that FDev have taken into account how important these minor factions are going to be to the players aligned to them and would therefore make them in some way hardier than normal in-game minor factions.
Personally, while I do have some issues with the way that Code and their allies enacted the Hutton blockade, and while I do have very serious issues with out-and-out griefing for the sake of it, I do feel that there should be some way for all of us to co-exist in the same Open space if we so choose, without fear of being subjected to unwarranted PvP (i.e. motiveless murder). But that's just my opinion. I'll also freely admit that I spend most of my time in Group these days simply because I know I can't afford to lose my ship too many times to unwanted griefing.