Cortana could go through rampancy and become metastable (in fact she might already be metastable). There are four stages of rampancy:Sadness,Anger,Jealousy, and (in theory) meta stability. The first stage is pretty much self-explanatory. In the second stage, Anger, the AI begins to hate everything around it and will try to enact revenge and free itself from programming constraints. In the third stage, the AI will seek to grow and develop as a person. In the theoretical fourth stage, the AI can be said to be a true "person". The only two AIs who may have reached metastability are 05-032 Mendicant Bias and Cortana.
Link: http://halo.wikia.com/wiki/Rampant