Regrettably it's usually the opposite. US foreign policy since 1945 is a good example, supporting one brutal, hated dictator after the other.
As long he's anti communist (this is what they feed media and masses) and more importantly, willing to work toward common (American) interest.
Case Mobutu Sese Seko, Congolese dictator: came to power after military coup (organized by CIA and Belgian government), only because
democratically elected leader was smart and dangerous man who worked for his country and opposed foreign interest. Mobutu stayed tyrant for quite a long period but he lost western support. They simply didn't need to support him any more because main threat has been dealt with.
Case Reza Pahlavi, Shah of Iran: He served a good purpose until USA came up with a different plan that included religious uprising which will create instability in the whole region. During Shah's reign
democratically elected prime minister was executed after he was overthrown in coup d'etat organized by Central Intelligence Agency. Guilty of working in best interest of his country which was directly jeopardizing foreign interest.
Case Muammar Gaddafi: Came to power in military coup. Stayed in power for quite awhile. As tyrant was regularly granted support of western countries. When western strategy in northern Africa and middle East changed and some of his actions started to pose a threat to foreign interest, he was brutally executed.
Case Josip Broz Tito: Came to power after WWII, was known for balancing between blocks which granted his country some advantages over other communist countries which were fully dependent of Soviet Union. Due to change in American politics mid 60s and some of his silly moves, he lost favor of the west. Which put his country into downfall which ended in shattering of Yugoslavia 10 years after his death. Was smart enough to avoid assassination but silly to think he's going to form third block consisting of undeveloped countries.
Case Slobodan Milosevic: Instrumental in fall of Yugoslavia, had strong ties with foreign intelligence agencies. When he finished his job, he was taken care of.
Case Saddam Hussein: Was instrumental in coup that removed Qasim from head of the Iraq state. Qasim was very much like Saddam but he made a mistake when demanding fairer distribution of oil money. By doing that he signed his death sentence. Saddam was chosen to get rid of Qasim but he failed and had to flee to Syria. From there he organized another assassination attempt which was successful. Took him five years to come back to Iraq and take the throne for himself. Went into war vs American allies in middle east, attempted annexation which was start of his demise. Later, to overcome economic sanctions he traded oil for goods, mainly with Russia. Not even a decade later he was branded as Satan, who possessed weapons of mass destruction and was brutally executed. All in name of freedom and democracy, strictly to protect life of innocent Iraqi. Has nothing to do with western interest, no no...
Do you see a pattern here or should I continue?