What is the result of damage to the chordae tendinae in the left ventricle?

Heart disease. The chordae are support structures for the mitral and tricuspid valves. When they are damaged, valvar insufficiency results. This can be severe enough to cause congestive heart failure either acute or chronic.
Leaky Valve. Usually, this leads to a leaking valve and, if untreated, eventually congestive heart failure. The duration which a person can tolerate a damaged chordae is dependent on the person's health otherwise, the cause of the damage, the amount of the resultant leakage, and the size and function of the left ventricle prior to the damage.