Not resignation
Abdication is not like resignation, but has a deeper sense. Abticating means relinquishing a position of power without a hope of ever returning to it. For example once a king has abdicated he can never become king again. Abdication has a somewhat negative connotation. Another frequent modern use comes in the phrase "to abdicate responsibility". Usually it means that a person or organisation neglected their duties through indifference or incompetence rather than as a conscious action. For example "delegation through abdication" is when a manager turns out to be useless and their staff are having to take responsibility in order for the business to run properly (rather than the manager skillfully delegating tasks and responsibilities).