Abandonment is the state of being forsaken or neglected by someone or something. This can apply to people as well as objects.
Abandonment can carry different connotations based on context. Children are often abandoned by parents who do not wish to take care of them. Members of a group often choose to abandon a particular member either to better themselves or because of the abandoned member's negative qualities. Banishment, a punishment where a person is expelled or abandoned by a group, was often one of the harshest non-physical punishments because of the psychological effects of loneliness that it causes in a person.
Abandoned items or objects are often such because of their obsolescence or negligence by their owner. Ideas or concepts may also be abandoned metaphorically because of their inutility or undesirability.