Does lack of communication destroy a relationship?

It can. Think about it in a business sense. Without communication, companies would have no way of determining whether their ideas and goals were being met. They'd have no way of resolving disputes because no one would know what the other felt. Without adequate communication, assumptions (often wrong) are made. Without communication, a business could not succeed. Same goes for relationships. Without communication, it's virtually impossible to know what the other is feeling. People must find a way to communicate with each other, letting others know their opinions and feelings on certain matters and offering solutions to problems.