"I'm just an ordinary man with nothing to lose." - Lester Burnham (played by Kevin Spacey) in the 1999 film American Beauty.
When Lester Burnham had nothing left to lose, he acted recklessly. He wasn't a bad guy, he simply decided that what he had in life wasn't worth keeping secure so he began to act on impulse and do what felt best at that moment.
When homeowners have zero or even negative equity they, like Lester, have nothing to lose. If there is no equity, there is significantly less motivation to continue to make a mortgage payment. This is certainly the case when they can rent a similar or even nicer home for a payment less than their current mortgage payment.
Conversely, equity motivates. Having equity in a home spurs an owner to make mortgage payments, even if their income drops or there is some other financial difficulty. Owners don't want to lose the equity they have already paid into a property. They have something to lose. They also have the ability to sell the home if they can no longer afford it, and turn that equity into cash.
Lack of equity is the number one predictor of homeowners that will default on their mortgage. This is why there is a great deal of debate regarding what an appropriate down payment should be to purchase a home. Conforming loans (Fannie Mae & Freddie Mac) offer as little as 3% down payments. FHA requires a minimum 3.5% down payment. VA requires no down payment for eligible veterans and active duty servicemen.
Housing industry groups and consumer advocacy organizations want to keep down payments low so that homeownership is possible for low-income and middle-class populations. Others want to see minimum down payments increased to 10% or even 20%.
Saving for a down payment is the number one obstacle for homeownership, so any increase will result in fewer new homeowners. But those homeowners will be motivated to continue to make mortgage payments since they will have "something to lose."