The following article contains spoilers from DCeased: War of the Undead Gods #2, on sale now.
Supergirl's new status as an agent of anti-life actually harkens back to an older story about her. In DCeased: War of the Undead Gods #2 (by Tom Taylor, Trevor Hairsine, Andy Lanning, Rain Beredo, and Saida Temofonte) the power of having an undead Kryptonian as a weapon was on full display. Supergirl wasn't just a participant in the attack on Korugar, she was a key part of Darkseid's victory. Her actions not only gave Darkseid access to a yellow lantern ring, but she also allowed him to kill Sinestro, and seize control over the Warworld.
In short, Supergirl has become Darkseid's zombified right hand. This actually ties back to Darkseid's early designs to transform Supergirl into the leader of his female furies and have a Kryptonian as both his sworn protector and attack dog. While in this alternate world he has succeeded in enslaving a Kryptonian to act on his every whim, this wasn't an isolated attempt.
There was a time, very briefly, when Supergirl was captured by Darkseid and brainwashed into becoming a female fury. Darkseid's goal was to have her lead his forces, but she managed to break free before she had committed any atrocities in his name. While that plan may have failed, the temptation of having a Kryptonian as his personal servant and weapon couldn't have been far from Darkseid's mind. It would seem that alternate versions of him had the same idea, but with more success.
By infecting Supergirl, Darkseid hasn't just gained a powerful weapon against his enemies, he has also gained a personal bodyguard. During the attack on Korugar, Supergirl was very much the vanguard of his assault. The first enemy encountered by the Green Lanterns was her, and she quickly went about dismantling their best weapon -- the Warworld. Or more accurately, she stole it for the forces of the undead, giving them an even greater capacity to unleash death upon the universe.
Later, when Darkseid engaged Soranik and her father, Sinestro, in battle, the three seemed to reach a stalemate when it came to unleashing their full powers. That is, it would have been had Supergirl not intervened, distracting the father and daughter duo long enough for Darkseid to kill Sinestro. In the process, Darkseid gained access to his ring, and even more power, all thanks to Supergirl.
In a strange way, everything she's done validates Darkseid's desire to have her as a fury. She has been incredibly effective, not only as a force of raw power but because the tactical use of her strength disrupts Darkseid's enemies long enough for him to win in the best possible way. In the few short hours he has had her, he's managed to decimate a planet, acquire a weapon of mass destruction, eliminate a dangerous rival, and even acquire another weapon for himself, all without any significant losses to his army. If this is Supergirl as an undead puppet, imagine what could have been accomplished if Darkseid succeeded in the main universe.