Maybe, but it’s harder to profit from it. A firm may be reputationally damaged, but what’s the incentive to cause that damage?

I think the Bloomberg Odd Lots guy wrote a blog post on this: you could attempt to short the stock but a) this leaves a paper trail b) the market might not know about the breach or believe you if you post you’ve done it. IIRC some hackers have tried to tell companies that they are legally required to disclose the breach to their shareholders to force market movements.