When a company “deleverages,” it means it is attempting to shrink the amount of debt on its books relative to its assets.
In some cases the act of deleveraging requires a company to sell-off/liquidate key assets in order to pay down debt, which ultimately means downsizing as well. A company may choose to deleverage as a strategic tactic, but often times they are forced to as a result of economic circumstances.
A recent example was in the aftermath of the 2008 financial crisis, when banks underwent a significant deleveraging period to increase their capital ratios, as required by new laws.