Employees working for companies with big debt loads were particularly vulnerable to firings when household demand collapsed in the last recession.

That's the conclusion in new research from finance professors Xavier Giroud and Holger Mueller, and it's exactly what's been worrying U.S. bank regulators for the past two years.

Giroud, a professor at Massachusetts Institute of Technology, and Mueller, a professor at New York University, note that falling house prices lead to falling demand. From that point, they ask: How do companies respond? They find that balance-sheet health matters.

When faced with plunging household demand, leveraged firms "do not (or cannot) raise additional external finance" they write in the paper.  "Instead, high-leverage firms reduce employment, close down establishments, and cut back on investment."

The market for high-yield or "leveraged loans," defined as debt that's typically issued by speculative-grade borrowers, expanded rapidly after the recession. Mergers and acquisition financing helped drive supply, while demand has been turbocharged by central banks driving down short- and long-term interest rates around the world to try and support economic growth.

Total outstanding U.S. leveraged loans swelled to a record $840 billion this year from $130 billion in 2001, according to Standard & Poor's Capital IQ Leveraged Commentary and Data.

Regulators including the Federal Reserve in March 2013 issued very specific guidance on what they would consider sound lending in this market.  They stepped up the pressure over the past year after issuance remained strong. The chart below shows the crackdown may finally be having an impact.

Their worry hasn't been so much that banks would get stuck with delinquent debt and replay the mortgage crisis of 2008. Leveraged loans are syndicated, meaning they are sold off to hundreds of different buyers.

The real concern has been that the financial system is creating a series of economic time bombs if companies are forced to slash payrolls in the next downturn to make their debt payments.

It's all about who can "weather the storm," Mueller said in an interview, "and that requires money." Firms with strong balance sheets were still able to raise cash during the recession. Firms with weak balance sheets had limited financing options and had to cut staff.