Berserk
A state of mind which is a harsh reality for soldiers in dangerous conflicts. Derived from the Germanic word "Bear-Clad", it is a rage named after Viking warriors dressed in bear furs, intoxicated by mushrooms and spirits, engaging in frenzied combat. Today, it is sometimes synonymous with blind rage or uncontrolled frenzy, as a soldier mindlessly fires off his weapon, regardless of proximity of friend or foe.
Testing when aliens are at 0 Morale shows that totally demoralized aliens berserk (as opposed to panic) ~36% of the time:
Min Ave ± SDs Max Count 1 5.72 ± 1.78 10 Percent 6.25 35.75 ± 11.11 62.5
Each test is the number of aliens that berserked (instead of panicked) out of 16 aliens at 0 Morale. There were 118 tests of 16 demoralized aliens (raw N 675/1888). My (MTR) guess is that the true value for this number (X-COM's target value) is 35%.
As you can see, there's a lot of variability. With a rate a little over one third, it's fairly common, too.
Percent berserking may or may not differ if Morale is significantly higher than 0 (but this takes more work to test).