As the comments above have been trying to get across, the prospective employer is offering to pay you for the bonus/unvested compensation that you would be losing by jumping ship right now to go work for them. They are not offering to buy any securities that you already hold, regardless of whether they're profitable or unprofitable.
Example 1. You participate in your current company's 401(k), and your company matches your contributions at 50%. However, the matching funds are not yours immediately; they vest in 20%/year increments until you have been at the company for 5 years. Let's say you've been there for 3 years and have contributed $50K to the plan. Your company has matched you at $25K, but only 60% of that ($15K) has vested. If you leave right now for the new employer, you're leaving $10K behind. So the new employer might offer to "buy out" (i.e. pay you) that $10K to help encourage you to switch now. You might then counter their offer by pointing out that if you stay where you are that $10K is coming to you tax-deferred, whereas their $10K signing bonus would be taxed. So you ask for $15K instead.
Example 2. You work for a Wall Street investment bank. Each December you receive a performance bonus. Since you began working there, your three yearly bonuses have been (in chronological order) $500K, $750K, and $1M. It's June, so you've worked halfway towards your next bonus. You have a lot of incentive to NOT leave your current employer. A competing employer may offer to "buy you out" of your anticipated bonus by giving you a $1.25M signing bonus (since you'd almost certainly not be eligible for a performance bonus during your first year there). You might negotiate with them and say "I'm on track for $2M this year", and then they would figure out if you're really worth that much to them.
So you can see this all has to do with the prospective employer trying to compensate you for any income you're already counting on receiving from your current employer. By jumping ship now you would be foregoing that guaranteed/expected income, so the competitor wants to remove that anchor that might be holding you back from making the move.
Stocks/options that you already own are irrelevant to the prospective employer. Since you wouldn't be giving those up by changing jobs, there's no reason for them to factor into the equation.