If "A Customer" doesn't want to talk anymore regarding any product or services! So how would we approach and satisfy the customer?

Leave him with gratitude, however be in followup with him. Just remember, a dry coconut can be broken with a stick also but you should know how to hammer it. 

There would be two scenarios which will be used to engage customer in such situation.

1) Carefully understanding the customer's opening statement and/ or the statement that he/ she used to reject the conversation.

2) Before initiating conversation as per Pt. # 1; Knowing Customer's niche/ segment is also equally which helps clarifying the general needs/ situation of that particular niche/ segment. This helps in re-establishing conversation/ contact with same customer even in those situations where customer has already rejected the conversation.

After having the understanding as per above mentioned, the most important part comes; which is to link the customer needs (identified through Opening Statement/ Niche) with the product features. Please note that in case of complaint scenarios (existing customers); this becomes partially valid since customer would have already gone through the mentioned phase. So, Tactful dealing does matter in those critical situations, i.e. more focus on Empathy rather than sympathy, and making creating realization of the situation will help protecting customer from churn.