The flexible thing that encloses all the living material in an animal cell is the cell membrane.

Here's why:

* Flexible: The cell membrane is made of a phospholipid bilayer, which is fluid and allows for movement and flexibility. This is important for things like cell division, engulfing nutrients, and releasing waste.

* Encloses all living material: The cell membrane acts as a barrier, separating the internal environment of the cell from the external environment. It controls what enters and exits the cell, ensuring the proper functioning of all the cell's organelles and processes.

Let me know if you have any other questions!