In the US in the past (pre-Enron) some companies blocked the ability to sell company shares by requiring 401K matching funds to be company stock. The employee had no ability to sell those shares unless they quit, retired, or were fired. Thats is no longer true today.
If the company is not publicly traded, even if the shares are vested, the only way to sell the shares is either back to the company, or maybe to other existing shareholders. In a private company it could be possible for the company to require, by contract, that officers of the company own a percentage of the company or invest a set amount in the company. When people say they are a partner they are expected to share some of the risk, and benefit from the gains. Think in terms of law firms and doctors practices.
But if the company is public, and the shares have vested, the employee can sell them at any time. They can do this in the open market. Of course if they are in the 401K or ESOP there are other rules, but they are clearly defined by those programs.
If the employee is in a position of having insider knowledge, then the buying or selling of shares has to be done while considering the insider trading laws.
In the case of a public company there can also be contractual obligations. It would likely include officers of the company. The board would want the CEO, COO, CFA , vice presidents and board members to be invested in the company. Those requirements would be clearly laid out in the contract.