If there’s no valid reason for termination on either side, then (in theory) the contract is not actually terminated. Of course, if both parties agree to terminate it, they can.
If one side disputes the termination, it can still terminate the contract in its own favor, citing improper behavior by the other party.
Ex. 1: A fires B for an improper reason. B terminates the contract, using Art. 14 to claim severance pay. Legally speaking, the date of termination should be the date on which B quit.
Ex. 2: B quits for an improper reason. A terminates the contract, using Art. 12 to absolve itself of responsibility. Legally speaking, the date of termination should be the date on which A fired B.
In either case, A owes B a 離職證明書 or 服務證明書. The only way out of that (if the job is subject to the LSA) is to avoid terminating the contract (i.e. A refuses to accept any form of termination until the end of the contract period).
How picky the NIA is, I don’t know.