Mortgage delinquency, if not remedied, can ultimately result in your lender foreclosing on your home. (This is true not only for the primary mortgage but also a home equity line or loan.) However, if making your payments is impossible, most lenders are much more interested in trying to figure out a way you can continue to pay your mortgage than foreclosing.
It is best to call your lender before you miss your first payment and be prepared to explain your situation. They will likely want to know what the cause of your hardship was, what your current expenses and debts are, and what steps you are taking to improve your financial situation.
