Hi HN,
I joined a startup a few months ago and my compensation includes a small amount of stock. The company recently provided a document for me to sign, which laid out the terms for the options they are granting me.
As part of this document, there is a clause describing a Repurchase Right for the company. According to this clause, the company is able to buy back at fair market value any quantity of my vested, exercised shares when I leave the company, or when I exercise my options after leaving the company.
Is this kind of arrangement common? Given that I have already accepted the offer and worked at the company for a few months, I don't think I have any ability to negotiate this. The offer letter specified that the options would be subject to this agreement, which I didn't realize or ask to read at the time, so I guess that's a lesson for me in acquiring every relevant document before signing.
That said (having used standard forms before) there are usually two terms with respect to shares: the repurchase right for unvested shares and a right of first refusal.
The repurchase right gives your employer the right to repurchase your unvested or unexercised shares after a timeframe (often 90 days) after you leave the company. There was a lot of excitement when companies like Pinterest extended that 90 days to several years, as it's very employee friendly. The amount they pay is usually the value you "purchased" them for, often the grant price (e.g., pennies per share).
The right of first refusal, which I believe you're talking about (given your market value statement) says that for the shares you own (exercised and vested) but have found another buyer for the company has the right to buy them first. The wording is usually very confusing about whether or not they have to match the external offer, but the basic provision makes sense: let the company buy back its equity rather than let some random new investor appear, but pay the (usually former) employee the same amount. Note that as above, there's some time period involved, so you don't get to just say "I found a buyer at $100/share, pay up by tomorrow or else".
Note that while I think you've misunderstood, it's totally possible that you've read your (highly unusual then!) equity contract correctly. Again, take them to a lawyer if you want to be sure rather than listening to some random person on the internet :).