What's the consideration for this contract?
Speculation: maybe the options they earn when they work there have some provision like this. In return for the NDA the options get extended.
For example, you may join a company and be given options to buy 10,000 shares at $5 each with a 2 year vesting schedule. They may begin vesting immediately, meaning you can buy 1/24th of the total options each month (or 614 shares). Its also common for a delay up front where no options vest until you've been with the company for say 6 or 12 months.
Until an option vests you don't own anything. Once it vests, you still have to buy the shares by exercising the option at the $5 per share price. When you leave, most companies have a deadline on the scale of a few months where you have to either buy all vested shares or forfeit them and lose the stock options.
Part of my hiring bonus when joining one of the big tech companies were stock grants. As they vested I owned shares directly and could sell them as soon as they vested if I wanted to.
I also joined a couple startups later in my career and was given options as a hiring incentive. I never exercised the vested options so I never owned them at all, and I lost the optios after 30-90 days after leaving the company. For grants I'd take the shares with me and not have to pay for them, they would have directly been my shares.
Well, they'd actually be shares owned by a clearing house and promised to me but that's a very different rabbit hole.