It also may be explicitly disallowed. I'm in a deadwood position on a company that's still private and the shares have a restriction that they can only be sold to the company or via a deal that the company brokers.
Humorously enough, while I was reading this thread, I got an email from the CFO of that company, who I haven't heard from in a couple of years now. My heart skipped a beat. :) Alas, it was not an heads up about a liquidity event...
Seems curious, though, that a CEO wouldn't want that 5% available to the investors at a reasonable discount. Versus the pittance that's being offered. Makes you wonder what else is afoot.
According to jacquesm upthread, who sounds like he knows what he's talking about, you could well get sued for damaging the company. Looks like the only reasonable option is to work with the CEO.
People that know better than me: How nuclear an option would it be to ask the investors directly?