why the alive cell can't eat itself?

Answer 1

Every cell has got organelles of self-destruction, the lysosome. These lysosomes contain a lytic enzyme, lysozyme. As lysosomes and other organelles(mostly) are enclosed in plasma membrane, lyspzyme cannot act on them.

When a cell becomes old or worn-out, or becomes cancerous, lysosome is stimulated to release lysozyme in the form of vesicles, which bind with the plasma membrane of cell organelles and release the enzyme in the organelle, thereby lysing it.

Answer 2

All cells capable of eating themselves would soon be out of the gene pool.