Whether a non-paid board member can be a subcontractor for the LLC or not depends on the terms of any operating agreements or "board by-laws" that you may have in place. You want your board members to be loyal to the company and looking out for the company's best interests first and foremost -- not just looking for a financial reward 'round the back end because they're not paid up front as board members. Generally, though, situations like this (what's known as an "interested transaction," because the subcontractor has a direct financial interest in its outcome) are permitted provided that
(1) They are fully disclosed to the rest of the board.
(2) The board has the opportunity to discuss the transaction and vote on it without the interested party being present.
(3) The terms of the deal are in the range of what would be paid if an outside third-party were hired to perform the services (also called "arm's length" terms).