Q:

"Being ran", "being runned" or something else? 

The past tense of run is ran.  However, you couldn't say something was being "ran" poorly i.e. the business was ran poorly.  However, saying "runned" would be wrong as well.  What would be the word to use in this instance:

The government will be prevented from being ____ properly. 

A:

The passive voice in English uses the past participle, not the simple past. 

Sing-sang-sung.  Song being sung. 
Ring-rang-rung.  Bell being rung. 
Do-did-done.  Deeds being done. 
Speak-spoke-spoken.  Word being spoken. 
Break-broke-broken.  Rules being broken. 
Run-ran-run.  Government being run. 

(Your confusion probably stems from the fact that for many verbs, the past participle and the simple past are identical, as in make-made-made, play-played-played, etc.) 

A:

The missing word is run.  The government will be prevented from being run properly. 
Not that prevention will be necessary - it will fail to run properly all by itself.  Governments always do.