The government is simply the gang that won (vs the other gangs).
If the government fails, then you briefly get anarchy and violence until people organize into groups and use more violence to quash the anarchists. This repeats until there is only one group remaining, and that group is the government going forward.
If the government fails, then you briefly get anarchy and violence until people organize into groups and use more violence to quash the anarchists. This repeats until there is only one group remaining, and that group is the government going forward.