Resignation of director from pvt co. having only 2 directors

Hello Members,

Please refer to following situation and assist in understanding the legal position:

One of the director in a private company has made some fraud in company's name without knowledge of another director.

Now since, the matter came into light, that guilty director had directly applied to ROC for his regisgnation stating some foul reason and blaming the other director.

As per new Rules, He had made the application in form 11 for the resignation. and company has recieved an email from MCA statis that such application is taken up for "Direct Approval". 

My queries are:

1. Since the company has only 2 directors, Can ROC allows one of the director to Resign?

2. The company, till date has not filed form 12 to intimate the ROC about the resignation. What could be consequencies under the provisions of The new Act of 2013.