Unions

What would the legal term be for when a collective bargaining unit (union) pursues a grievance through multiple steps over a period of time? The word I think of is that they gave the grievant (union member who is being represented) ASSURANCE that the union backed the grievance. ASSURANCE does not seem like the correct legal term though.

my question is what is the legal claim/or grounds/statutory on a labor union neglect on representation on a false accusations,wrongful termination,defamation/libel, these accusations and termination where done to one of her/union member by the employer. The union din''t do anything to defend its union member.Employee is now suing the union. Plaintiff needs to instate a claim.