1. Why are they looking externally for a candidate instead of an internal candidate that is more familiar and has a track record with the company than a brand new leader?
2. What were the specific expectations of the incumbent leader and how long have they been in the position? Someone needs to explain what happened and realize that this very same dynamic could happen to you. If nobody communicates with a person that they think their communication is bad, it's a passive-aggressive culture that won't lead to good outcomes more often than not, especially long term.
3. What's the turnover rate for the team? Don't believe whatever they tell you, but make a note. Then try to assess its veracity based upon Linkedin stalking of both currently employed and past employees.
4. What's the highest level of management that is in agreement of replacing this person? If something came from really high up, I'd ask if there was a specific incident. I've seen people let go because they made exactly one hot-headed executive very angry for flippant reasons and while everyone in management that actually knew these people were fine, their hands were tied. That kind of leadership style is micromanagement oftentimes and the toxicity and blame games will eventually make their way down the longer the leader stays.