The major falsifiable prediction is that reminding people of their own mortality will cause them to increase the strength of their psychological terror defense mechanisms, which may include culture, religion, or social ties. Here is a literature review of the subject from 2010. According to the review, the theory hasn't been falsified:

"MS [mortality salience, i.e. death reminders] yielded moderate effects (r=0.35) on a range of worldview- and self-esteem-related dependent variables"