I believe she is a high ranking official in the Ministry of Welfare, the department that oversees the Sybil System and Crime Bureau. While visiting Kougami, Akame tells him Ginoza is "petitioning the top brass and investigating right now". I assume that woman is the top brass he was petitioning.
And they are well aware that the Sibyl System isn't perfect huh? <___< I wonder who exactly that woman is, at the end it seemed like she knew Makishima from before this incident.
Now that we know there are other cases like Makishima and how they're treating them, the System appears even more questionable....
The mirror images of each other, I think. Makishima would probably be termed ASPD in real life. For most people, even criminals, breaking the law would cause some sort of stress reaction. Fear, worry, guilt, anger, denial, hostility. At the very least, most criminals would be afraid of being caught. ASPD is a neurological disorder, neurotransmitters responsible for emotion do not work properly. Makishima simply does not have the full range of emotions needed for his criminal coefficient to rise. He can commit heinous crimes without any strong, emotional reaction. She, on the other hand, does have the full range of emotions, and does react naturally to stressful situations. But she has such good coping skills that she is able to manage high stress situations. There really are people like her in real life too. She fits the profile of a hostage negotiator in real life, able to remain calm at all times, think clearly, stay in the moment, and rationally deal with a life or death situation. While the results are the same for both, the reasons are very different.
Tsunemori is exactly one of the cases like Makishima, just that she's not using it for criminal acts. They are just too similar - I remember Makishima's Psycho-Pass went up too when he killed her friend but slowly went down every time Tsunemori was pointing the Dominator at him, just like what happened when she tried to remember the scene and her PP went up temporarily.