Does HP loss in ferocity state is the same as when dying?
A creature with ferocity remains conscious and can continue fighting even if its hit point total is below 0. The creature is still staggered and loses 1 hit point each round. A creature with ferocity still dies when its hit point total reaches a negative amount equal to its Constitution score.
Can I stabilize to end the HP loss?
Yes, but performing strenuous actions, like attacking, will cause you to lose 1 hit point and begin dying again as normal.