Mitochondria can stop working for a couple of different reasons. They contain their own DNA separate from the DNA in the nucleus, changes in this mitochondrial DNA (mutations) stop some of the proteins in the mitochondria from working properly. When this happens the whole mitochondria will stop working properly.
Other changes in the cell that can damage the mitochondria might also stop them working properly, for example oxygen species. A lot of the other proteins in the mitochondria are encoded by genes in your chromosomes so mutations here can also make the mitochondria stop working.
When mitochondria aren’t working properly any more they are broken down by our cells and the components can then be reused, In Parkinson’s disease the mitochondrial stop working due to a combination of all the things i mentioned previously.