Yes, there is a chance that the value will be negative. But the question whether or not stable depends on the generator itself - that's why it is needed to have detailed modelling of generators and its parts (ex. governor). But most cases is that negative is unstable.
It is incomplete if you talk only about the rotor angle. You should its value based on a reference. Remember that the theta in the formula is a difference between two angles. If E1 has negative angle and E2 is zero (reference) then likely that the power flow is backwards which is unstable.
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