If the employee gives two weeks notice, not 6 months, then the employee can be responsible for damages to the employer. I have no idea what damages apply in your situation, but think lost profits and additional hiring costs because of short notice (not costs the employer would incur anyway if you gave 6 months notice).
If the employer breaches the contract there is an argument for constructive dismissal and as such the 6 months notice clause is not operative because you did not resign. Not an easy one for non-lawyers and sometimes one or two seemingly small facts can make all the difference at court as to whether a finding of constructive dismissal is made out.