Ultraexacting cardinals are among the most recently introduced large cardinal axioms, sitting near the upper reaches of the large cardinal hierarchy and defined by extremely strong elementary embedding and reflection conditions. A central open problem is whether these cardinals can survive arbitrary forcing extensions, meaning whether one can start with a universe containing an ultraexacting cardinal and apply forcing to change the universe without destroying that cardinal's defining properties. This is not known even for many simpler large cardinals, and for ultraexacting cardinals the problem is almost entirely unexplored. Specifically, which forcing notions are safe in the sense that they preserve ultraexactness, and which ones inevitably destroy it?