What keeps mitochondria from multiplying out of control?
I'm guessing at the motivation for your question -- In the evolutionary history of eukaryotic cells, mitochondria were once free-living bacteria.  What prevents them from acting as intracellular pathogens and replicating out-of-control?
Yes, by endosymbiotic theory 1, mitochondria were once free-living prokaryotic organisms.  This is evident because they have their own DNA, undergo replication by fission, and have characteristics similar to proteobacteria.
However, some of the genes required for mitochondrial replication have been moved to the nuclear genome.  This means that, while mitochondrial replication is not necessarily tied to cell replication, factors encoded in the nucleus are necessary for mitochondrial replication.2

https://en.wikipedia.org/wiki/Symbiogenesis
Ali, et al. Nuclear genetic regulation of the human mitochondrial transcriptome. eLife 2019;8:e41927.