As a general rule, individual members are not liable for actions they take on behalf of the church, such as voting at board meetings. Most jurisdictions also allow the church to indemnify board members when there is a complaint, meaning to pay for their defense and not make any claim on behalf of the church against them.
However, sometimes board members are accused of intentional or criminal misconduct, in which case they will be personally liable. One emerging issue that has surprised board members is that they can be held personally responsible by the IRS for a tax debt if they were part of a board that approved unreasonable compensation for an employee of the church.
A board typically acts by majority rule and no single member is going to be liable for board actions. But, if the board was engaged in intentional or criminal misconduct, such as using church funds for personal gain, then they may be responsible. A board member owes the church a duty of loyalty, meaning not only is s/he supposed to only do things that are in the best interests of the church, but s/he must also make sure that other board members do the same.