Chordau tendiniae. The "fibers" are called "chordae" and are similar in function to parachute chords. They prevent the valve leaflets to prolapse (tricuspid and mitral), holding them back just like a parachute chord prevents the parachute from flipping up. If these chords break, the valve will leak. Surgical fixes include annuloplasty (narrowing the valve ring), repairing the chordae, and valve replacement.
Fibroelastoma? If you mean papillary fibroelastoma which are benign tumors that typically involve one of the heart valves, the treatment depends on symptoms and the size. Surgical excision is at times recommended for relief of symptoms.