What happens when a government is aulted or overthrown?

There are so many factors not known in your question. For instance Kuwaitt was overthrown by Saddam and the world responded by kicking Saddam out of Kuwaitt simply because we (and other nations) had made agreements with Kuwaitts government to back them up in a time of need. So if the dictator or democracy had such an agreement with us it is likely we might intervene to protect them.