In the past the stock was supported by the dividend so it's no surprise what occurred after it was cut. Here's another way to look at it through the lens of their leverage. As the leverage increased so does risk which is reflected in the chart below. As they lower their leverage it will not be the dividend that helps prop up the price but their fundamentals. IF they get the leverage ratio below 3 the chart seems to infer a price above 30 of course it will take years for this to playout so in the meantime it's going to be a bumpy ride.
The cut was like a two-edged sword. In order to get to a reasonable leverage ratio in the near term (which will result in credit upgrades along the way which equals better terms on new debt) they had to cut which had a short term negative affect on the stock in exchange for a better longer term outlook IF their execution is in line with their rhetoric. The chart is as of Q1. (CTL announced the LVLT deal at the end of 2016)