There were two pre-conditions to the LBO craze.
The first is that there should be a supply of companies whose assets were worth more than the company's stock.
The second is that you need a supply of people who are willing to buy large amounts of high-risk bonds at a reasonably steep premiums. (These are popularly known as "junk bonds".)
What you then do is spot a likely takeover candidate, float a junk-bond issue, use the financing from that to take over your candidate, sell off the pieces, use the revenues from the sale to pay off the junk bond, and skim off some profit for taking the risk with other people's money to destroy someone else's company. In other words you don't get credit from a bank lending you money, you do it like the big boys do by selling bonds.
The fad faded because the necessary economic pre-conditions ceased to exist. Oh right, and also a number of the key operators landed in the slammer due to an upcoming lawyer named Rudolph Guiliani...
Cheers,
Ben