I would say this is fine, this position will likely inherit the bad juju from the previous candidate and should go into the position eyes-wide open. What they need is a person who can acknowledge previous mistakes and make incremental changes to guide the team to the right operations. They want to understand what about this candidate will make the situation different from the last candidate and in order to do that they need to discuss the previous employees shortcoming.
I actually enjoy replacing someone who is a poor communicator because you have a real chance to influence direction and growth just by acting like a normal, decent person.
To answer the original poster's question - if you have to ask this question, it's very likely there are organizational challenges. In fact, at every company there are organizational challenges, team challenges, your job as a leader is to address them. If you want to only work for great teams and never have to deal with challenges, you should consider not being a manager/leader at all, then you don't have to worry about them.
I would pay more attention to whether the company itself is financially stable, growing, hiring and innovating. If not, run.
I think it would depend on the 'why' of the firing. However to mention it at all without telling you something like "You're replacing X, who is being investigated on criminal charges for/related to..." IE you have a legacy mess that you'll be cleaning up; yeah that's extremely unprofessional and likely unethical.
I actually enjoy replacing someone who is a poor communicator because you have a real chance to influence direction and growth just by acting like a normal, decent person.
To answer the original poster's question - if you have to ask this question, it's very likely there are organizational challenges. In fact, at every company there are organizational challenges, team challenges, your job as a leader is to address them. If you want to only work for great teams and never have to deal with challenges, you should consider not being a manager/leader at all, then you don't have to worry about them.
I would pay more attention to whether the company itself is financially stable, growing, hiring and innovating. If not, run.