It depends upon the type of leader one was. The range of options is wide open.
If you're Idi Amin, you live out your life in exile.
If you're Slobodan Miloševic, you live out your life in prison.
If you're Muammar Gaddafi, you get killed by a group of opposition rebels.
These are obviously all examples of bad leaders coming to an end, but exile, prison, or execution appear to be common options.
Mohammad Mosaddegh was by most accounts a good leader who ran afoul of US and UK petroleum interests. After the CIA and MI6 orchestrated a coup, he was overthrown and lived out his life under house arrest.
In Israel, David Ben-Gurion, Yitzhak Rabin, Yitzhak Shamir, Shimon Peres, and Benjamin Netanyahu served non consecutive terms as Prime Minister. People revolve through different positions in the government, so after leaving office as Prime Minister one is not necessarily done with public life.
Harry Truman lived a very modest life after the Presidency. Presidents since have lived quite varied existences after the Presidency.