Explanation

Your clue is that the scandal here is so severe that the company can save itself only through the rather extreme measure of “mass firings.” Bogged down and mired have the sense of being stuck in something (a bog and a mire are both physical things — swampy, quicksand-like patches).

Note trap answer wallowing — only a person or animal can wallow (and anyone wallowing wouldn’t want to “regain favor” anyway).

Hence options Bogged down, mired are best fit!