In short, yes, you can liquidate the company and force this issue. You can also protect your investor from risk, but why would you want to if you utilize the liquidation process to your advantage?
In regards to the liability for the film, there is the possibility that some residual liability exists for the owners of the film, yes, personal liability. However, if the film was first displayed some years ago, it's possible that the statute of limitations and estoppel issues preclude you from any remaining risk of considerable monetary damages (unless you modify / remake the film, or if you begin the distribution of the film in new locations). In other words, there is always risk, but your risk here is likely remote.
To force the issue of buy-out options and to get the ball rolling on this issue, you need to review the liquidation and wind-up provisions of the operating agreement, and identify the process for liquidating the assets of the LLC. In the liquidation process, as is common with the wind-up of most LLCs, it's likely that the film will be offered for sale to the public, and anyone can bid for and purchase the film (including the filmmakers). You and your partner (filmmaker partner) could offer to purchase the film, and exclude the hold-out investor from this form of ownership. Upon the conclusion of the sale, as is common with LLC wind-ups, the distribution of the proceeds from the sale would then be made to each of the investors pursuant to the agreement, and the LLC could then be dissolved. You may also have reserve accounts that would be closed and distributed to investors, why not avoid the $800 annual liability and take the remaining money as a final distribution? You could also pay for the LLC's lawyers fees out of any reserve accounts / proceeds from sale if you incurred these fees during the sale process or liquidation of the LLC .
To address your question more directly, I'm not sure why you would want to indemnify your hold-out partner, but you could if you wanted to. I would consider utilizing the liability issue to your advantage to discourage the hold-out investor from further participation. It is not your duty or obligation to indemnify or defend an interest holder in the film, but you could protect him from risk if you had to. Also, keep in mind that promises of this type are only as good as the promissors (If you have no money, how can you defend your investor?).
As an aside, did you create the film as a work for hire or was there an assignment of a pre-existing film to the LLC? Does any of the documentation identify any residual rights in the filmmakers, e.g. the right to limited display, or reserved moral rights? Would this satisfy you as filmmakers if you have these, or could have these? Moreover, if you plan to liquidate, you could ask the LLC to allow the filmmaker to retain these residual rights in the film, and sell the film to the subsequent purchase (assuming the filmmakers are not the subsequent purchases) with the carve-out rights of the filmmakers to enjoy the film in the limited ways you contemplate.
Plan for the contingencies and be creative with your solutions (Do as we lawyers do.). Also, be more considerate of your own interests and evaluate the bargaining position that you have with your hold-out partner. If you have a hold-out partner making waves, make sure you follow the proper procedure for the decision-making, and utilize the quorum of the other investors to encourage cooperation.
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