I haven't played this game in a while so I was re-reading the rulebook today and something drew my attention. Apparently I can build a faction location without a Foundation, provided I discard one of the common locations I had already built? So there are 3 ways to build a faction location: 1. raze a common card from your hand and use it as a foundation (by using 1 raze token) 2. raze a common card from the other player and use it as a foundation (by using at least 2 raze tokens, depending on whether she protects her locations or not) 3. simply discard one of the locations that you've already built.
Actually, you can only build a faction location by following way #3 from your list of possible methods. (Use a foundation from your own tableau of cards. This can either be a location you built or a foundation you have in your tableau because someone else razed one of your locations)
When you raze a card from your hand, the card is discarded (p.9 of the rules under Razing). It therefore isn't available to use as a foundation.
When you raze an opponent's location, they keep the foundation and can use it for a future faction building (they also get one wood). You only get the raze resources in the upper-right corner. After all, you are only looting the place for resources and aren't carrying the foundation away and back to your village!
1. and 2. = nope, you can't raze from your hand or an opponent and then build on that.
the alternate way is: an opponent has razed one of your buildings and you turned the card over (and you received +1 wood in the process and got a foundation symbol at the back) - that one can be discarded for a faction building.
other ways of building faction buildings without a foundation are only possible with certain action locations.