Use the noun ouster to talk about the process of forcing someone out of a position. If your city's mayor is pressured to leave office, you can describe it as her ouster.
When someone is dismissed or strongly influenced to abandon a position or quit a job, it's an ouster. A politician is often vulnerable to an ouster, when others are vying for her position, but your boss at work could also be subject to an ouster if his managers conspired to eliminate his job and force him out. Ouster once meant "kick out of one's house or property," from the Old French word oster, "take away, evict, or dispel."