you cant build new citis and admin centers

In the later versions of galciv, food is basically just another resource like Durantium. There has never been a consequence to negative resource values other than simple math (i.e. if you are at -2 food and build a farm to get +2 Food, your total balance would be 0).

So you can technically trash all of your farms once you have all of your cities, and free up that space for better stuff. lol

Like in other games, it just prevents you from building more.

Yes you are right.  But the cities you already built with that food will stay and the approval will be the same.. .

The reason why I post it is the following: in my current game my neighbor was a allied partner until I found one planet with 5 and one planet with 4 food tiles in his space. At this point I don't had much food. My complete strategy changed when I found this planets. All them cities based on this two planets. 

So I am going to invade. But the planets was very easy to invade. No legions or safety fleets were there. The neighbor planet without anything on it was saved by a strong fleet. After invading the neighbor faction still have all the cities which was built based on the food. 

With approval for negative food balance them cities were gone and/or the approval had to be much fewer. 

You should have to have the food for the cities you have... It would be a very deep experience I think.. 

ah yes, I've seen the negative D as well, building both legions and synthetic pop, though not a big deal for D as it will replenish 

food is not a resource like D or the others though - it is static and global and only needed to BUILD a city, not maintain it.

I don't mind negative food not having a penalty, I do agree that it would be a cool addition.  

think of it like this ... cities are always self-sustaining when built.  The population builds roof gardens, or the government subsidizes crops.  The food is only needed until the city is self-sustaining (built).  It is not a bug, it is not a big deal.