Employee-investors are very common. There are three ways employees can own shares of the company they work for, (in additon to investing with a stock broker).
Many companies offer an Employee Stock Ownership Program (ESOP), where they can choose to have some money taken from each paycheck and receive shares of stock. By signing up to take the money out of their paycheck directly, employees don't need to contact a stock broker or pay commissions, and the money can add up quickly over time. For example, and employee who signs up for just $25 a week will have invested $1,300 in their company's stock after one year.
Many companies also offer Stock Options. These options are the opportunity for the employee to buy shares at some point in the future for a guaranteed price (called the "Grant Price" or "Strike Price"). This price is gauranteed no matter what the ACTUAL price is. For example, a company might offer certain employees the option to purchase 1,000 shares at $10 a share on December 31. If the price of the stock is $30, the employee can buy $30,000 worth of stock for only $10,000. If they sell right away, they'll make an immediate profit of $20,000!
It is common for new companies (especially internet and technology companies) to use Stock Grants as well. With a stock grant, a company simply gives shares of stock to employees (typically in exchange for a lower salary). It saves the company money, and offers employees the opportunity to make a lot more money than they could earn in their regular paycheck. Since it went public, over 1,000 employees of Google are millionaires with their stock, but that's nothing compared to Microsoft, who has over 12,000 employee millionaires!
Regardless of the way employees acquire shares of the company, the shares are theirs to keep even if they leave the company.