Here's why:
* Simple diffusion relies on the concentration gradient of a substance. This means that the substance moves from an area of high concentration to an area of low concentration. This movement is driven by the inherent random motion of molecules (kinetic energy), and doesn't require any energy input from the cell.
* Active transport, on the other hand, requires the cell to expend energy (typically in the form of ATP) to move a substance against its concentration gradient. This process relies on specific proteins embedded in the cell membrane and will cease to function if the cell dies.
* Facilitated diffusion also requires proteins to help move substances across the membrane. However, these proteins are passive and don't directly require energy. While facilitated diffusion is still affected by the cell's state (e.g., damaged proteins may malfunction), it's not entirely dependent on active cell processes.
Therefore, even after a cell dies, the concentration gradient remains, and the passive movement of substances across the membrane through simple diffusion will continue.