"Company stock plans are increasingly viewed as a top  employee benefit and can play an important role in an employee's overall financial health," Mark Haggerty, head of stock plan services at Fidelity Investments, says in a statement. Haggerty adds, "Employees often use these plans as a savings vehicle alongside their 401(k), but money from an ESPP can be used to address short-term expenses and financial needs and help workers avoid the need to tap their 401(k)."

Fidelity's analysis checked three employee actions regarding their shares: whether employees held the stock for the three-year period, sold their shares at some point or sold some shares while keeping the rest.

Compared with similar research on employee behavior from 2014, the findings indicate that, unsurprisingly, market conditions influence employee behavior, with 50 percent selling all their shares into a rising market over the research period, compared with 48 percent in 2015.

In addition, employees receiving a bigger discount on the stock when they buy it are more likely to sell it.

Workers who were able to buy company stock at a 15 percent discount were 10 percent more likely, at 51 percent, to sell all their stock than the 41 percent who bought their sock at a lower discount and then kept all the stock they bought.

And while older employees are more likely to keep their stock, compared with younger employees, the percentage of workers between 50 and 60 years old who sold all their company stock rose to 44 percent from 2014's 41 percent.

Also, among employees 60 years or older, the percentage who sold all their stock increased to 38 percent, up from 34 percent in 2014.