Is the main shareholder responsible for misconduct of a limited company?

If by "limited company" you mean "limited liabiity company," then the whole point of those companies is to protect the shareholders from the company's liabilities. So generally no shareholders are liable for claims against the company, as long as the company has followed its corporate/LC formalities and the "corporate veil" can't be pierced.

It's usual for a patent license to prohibit the licensee manufacturer/distributor from competing with the licensor.

If Y is breaching the contract and infringing on X's patent, Y can sue X, but unless the majority shareholder
personally guaranteed the license or the X didn't follow it's own corporate requirements, can't sue X's shareholder.

It's difficult for a U.S. company to sue a company in Hong Kong, as IP laws are not enforced in Asia like they are here. Associating local counsel is nbecessary and might provide some help.

This sounds like a complex situation, nd there are probably many more facts that need to be disclosed and evaluated to assess this problem. Consult an IP litigator for specific advice.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.