It was first suggested in the 1960's that mitochondria evolved a symbiotic relationship with prokaryotic cells. That would have been the first step toward what we now call a eukaryotic cell. The process is referred to as endosymbiosis.
Endosymbiosis with the mitochondria suggests that it could potentially live and work without a host cell. Or they did at one time. There are three characteristics of mitochondria that support that hypothesis.
1. Mitochondria have their own cell membranes. Not all cell organelles are membrane covered structures. The mitochondria is . . . just like cells themselves.
2. Mitochondria has its own set of circular DNA. It is passed down from mitochondria to mitochondria and is separate from the host cell's genetic information.
3. Mitochondria can reproduce themselves by pinching itself in half. That's basically the binary fission that bacterial cells do.