"fiddle while Rome burns" is an idiom meaning to engage in trivial or unimportant activities while neglecting a serious or dangerous crisis that requires immediate attention. The phrase suggests irresponsibility, indifference, or a lack of concern for pressing problems, where someone is focused on minor tasks instead of the major issue at hand.
The idiom is rooted in the legend that Roman Emperor Nero played his fiddle (or lyre) while the city of Rome was destroyed by a great fire. While historical accounts suggest Nero was not in Rome during the fire and was involved in relief efforts, the story became a potent symbol of a ruler's callousness and indifference to his people's suffering.
This idiom implies someone takes no action in times of crisis.
While the company faced bankruptcy, the CEO seemed to be fiddling while Rome burned, focusing on office renovations instead of finding a way to save the business.