When you break, it'll still drop all of it, with the appropriate tools. Reproducible in the Vanilla environment, simply just break something that is two block high.

Steps to Reproduce

1. Place a door on the ground;
2. Switch to survival mode (if you are not in survival mode);
3. Start breaking the bottom part of the door;
4. The bottom part of the door will start to crack, but the top one will NOT start to crack, even if you mine the door until it breaks;
5. This also applies if you break the top part (the bottom part will remain unbroken instead)