Just to play devil's advocate, surely their approach is more rational than that. They're probably looking at it from the perspective that the business needs to have a profit margin of X in order to justify investing in it.
They probably do understand that cutting costs impacts company culture and morale. But shutting the company down probably impacts that much more.
They do understand that cutting costs will have an impact on culture and morale, they just think the marginal benefit exceeds the marginal cost. Keep in mind, PEG managers are chasing a carried interest bonus which they only achieve after covering the minimum return promised to their investors. Plus, leveraged buyouts--which PEGs frequently use--increase a company's risk of failure. Everyone's under intense pressure to perform.
They probably do understand that cutting costs impacts company culture and morale. But shutting the company down probably impacts that much more.