To add to my previous post, I have done phonon calculation for the graphene structure optimized using the tersoff_C_2010 classical potential, and I have not found any negative phonon frequencies for this optimized structure.
For hydrostatically-strained structure of graphene, the ATK-Classical calculation suggest that there exist a few pnonon frequencies having negative values. This might be due to the fact that strained graphene is more prone to buckling, i.e., structural large-scale instability; graphene rippling is known to take place in experiment on suspended graphene. One can not however fully rule out that there exists a bug. We will investigate this in more detail.