Dear Sam,
Mutual trust and confidence is the invisible common thread that keeps the employer and employee associated for any length of time. But, it is always hard to prove as to who lost the trust and confidence, the employee or the employer. There is no hardf and fast yard stick to meansure trust and confidence of any party. So, even if departmental/ domestic enquiry is held, the upper hand being of the employer, the employee only can be adjudged to have lost the trust and confidence of the employer. Even if due formalities are observed, in that respect nothing can be be substantiated justifiably.
But, your query seems to be half-baked with particular reference to the terms, "if the employee terminate immediately without due process." Assuming that the company has not adopted the due process of termination, as may have been prescribed in the terms & conditions of employment notified through offer letter or appointment letter, about implication, I can say that except the liability of the company to compensate the employee with the notice period pay, no other liability would rest on the company. But, if the termination letter does not specify the reason of loss of trust and confidence, the company can be made liable to pay gratuity also, if becomes due, as per the law.