If my company declares bankruptcy, do I have any special rights in my restricted stock or RSUs?
While restricted stock or RSUs still have value even when a company's stock price is lower than the grant price (stock options would be underwater), any type of equity grant can be worthless if a company goes bankrupt. That is one of the many lessons of litigation stemming from the bankruptcy of Lehman Brothers back in 2008. It was the largest corporate bankruptcy to date, and lawsuits relating to it are still playing out.
In the case In Re: Lehman Brothers Holdings Inc. (2017), the 2nd Circuit Court of Appeals confirmed that in a corporate bankruptcy RSU-holders do not have any preference over general creditors in the distribution of remaining corporate cash. Previously, the original decision in the lawsuit, made by the United States Bankruptcy Court, was upheld by the US District Court for Southern New York in 2016. It reasoned that RSUs meet the legal definition of "equity securities" and that employees with RSUs should therefore be treated like other holders of equity in Lehman Brothers. The contention that employees with noncompete agreements resulting from a merger should have priority over general creditors was similarly rejected. This outcome follows the reasoning set forth in a 2006 decision involving employee stock options in the notorious bankruptcy of Enron.