What do you do when all your attempts to correct a subordinate fails? You have given him sufficient time and now you have to take a decision and ask him to resign.
What will you further do, when he suddenly, also begins to exhibit disloyalty? There are times when you have to be ruthless as a leader. If you are not ruthless, it will confuse your other team members working for you.
During these times, you also need to communicate about this wayward team member to the others in your team. If you do not communicate, the only message they may get will be from that wayward employee. What he will tell about you and the situation will not be the one corresponding to reality.