The theory you're referring to is called the endosymbiotic theory. It proposes that eukaryotic cells (like animal cells) evolved from prokaryotic cells through a series of symbiotic relationships. Specifically, it's thought that:

* Mitochondria, the energy-producing organelles in eukaryotic cells, were once free-living aerobic bacteria that were engulfed by a larger prokaryotic cell.

* Chloroplasts, the organelles responsible for photosynthesis in plant cells, were once free-living photosynthetic bacteria that were engulfed by a larger prokaryotic cell.

In these scenarios, the smaller prokaryotes were not digested but instead lived within the larger cell, benefiting from the environment and protection provided by the host cell. Over time, the engulfed prokaryotes evolved into the organelles we see today.

So, to answer your question directly, the theory suggests that aerobic bacteria were engulfed by prokaryotes, eventually leading to the development of mitochondria and animal cells.

It's important to note that the endosymbiotic theory is widely accepted, but it's still a theory and ongoing research continues to refine our understanding of eukaryotic cell evolution.