They only have 1 hp after that. You could finish them with your bullets' windshear.
Fun fact: That is literally how the stock works.
EDIT: I won a Multiplayer match! Woo. And apparently, after checking the Rankings, I played against the number two ranked XCOM multi-player. So I took out the Number 2 XCOM player with an all-berzerker team. Neat. I learned a lot.
Lesson #1: Do you know what happens when a Berzerker actually hits you? They have a RIDICULOUS stunning rate. They are like, Stun Lancers on steroids. I knocked out (not killed, just knocked out) half the enemy team. In Single, that would be annoying, but since unless you have a medic unconscious is as good as dead, that translates to a chance to instantly kill any opponent you actually kill. Positively absurd. Even when they don't knock unconscious, they disorient.
Lesson #2: Berzerkers are not OP. They aren't. Having taken an entire team of Berzerkers on a match, they miss a lot (with venom, I'm taking 45% chances to even hit), they are weak to the box strat, and they CANNOT use the rangers dash-and-attack, meaning, like faceless, they have to blue-move to the enemy to kill them. Fortunately, if they get enraged the range of their blue move is enormous, allowing you to attack from a fair distance away. They also do poor damage, which means if you faced something that isn't organic they'd be pure target practice.
Lesson #3: Chrysallids are powerful, but not OP and might be better then Berzerkers (which are more expensive), although in a straight, mano a mano fight the Berzerker wins by a long-shot due to greater health. I was shocked to learn that A) their venom works on aliens, and B) they can make a cocoon out of aliens! That makes low-health aliens (looking at you, Sectoid) incredibly vulnerable. I also learned exactly how Chrysallid cocoons work: if you let them survive, they pop out one Chrysallid every turn (I think for at least three turns?). The chrysallid that pops out has lower health, but also can move on the turn it pops out, and so is very efficient at spreading more poison to make more cocoons.
That is all balanced out by having a melee hit rate: they only hit 75% of the time, and that is
not consistent damage. The entire reason I won and he lost is practically all his chrysallids missed their attacks except for one (or two?), and so they never really had a chance to turn my team into incubators. After I took out the four Chrysallids (and one viper who was just totally destroyed), I chased his Gunslinger around the map and had to put down the Chrysallid cocoon that spawned when one of my berzerkers succumbed (I couldn't destroy it in one turn, but the Chrysallid that spawned missed). Then I chased his gunslinger some more. By the end I was down to two Berzerkers, but they were both enraged and pummeled him. Actually they didn't: I tried to, but he dodged, and
then got knocked unconscious by the attack that he dodged.
I also got to chat with the guy, which was pretty cool. Overall, the dice were in my favor. I think I will roll with a Chrysallid squad next, but it's just so much fun to forget about any sort of tactics save placement and CHARGE the enemy.