Personally, I would run like the wind away from this place.

While it may seem "reasonable" in some regards, this leaves you liable for $10's of thousands potentially owing. If you have home/renters insurance contact them to discuss this liability and if it is covered and for how much. Then I would see if you can find out if there is any past issues with this complex and the management company.

No apartment is worth being financially devastated or worse. Just make sure you protect yourself just as much as these people are trying to protect themselves.