Can you claim bankruptcy and still keep your house?

It depends on the amount of equity you have in your home as well as other factors.  You should consult with a bankruptcy attorney who will then be in a better position to advise you.

It depends on the type of bankruptcy, as well as specific factors of your situation. Generally, in a Chapter 13, or reorganization, bankruptcy, a mandatory plan is worked out to pay your creditors as much as possible over several years; you keep your home. In a Chapter 7, or liquidation, bankruptcy, the majority of your assets (including potentially a home) are sold to pay creditors as much as possible immediately. However, neither bankruptcy necessarily overrides a secured lender's interest (e.g. a mortgage), so another wrinkle is that you may still be on the hook for your mortgage as well.

You should consult with a bankruptcy attorney to see what your best options are.

It depends.  In a Chapter 7 case, while you will lose assets but get rid of debts, you can either formally reaffirm the mortgage loan or, in some judicial districts, just keep making payments.  If your home equity is larger than the state's homestead exemption, Chapter 7 is not the choice since you would probably lose your home.  If you fall behind on payments, and have some equity in your home, Chapter 13 bankruptcy may be a better choice for you because it allows you to pay off the mortgage arrearages (missed payments) over time and therefore face less risk to losing your home to the trustee.  A critical consideration in a Chapter 13 case is whether a debtor whose home loan is in default can make the larger mortgage payments (the missed payments plus resuming the original payments) over the repayment period.  Finally, if your home equity is larger than the state's homestead exemption, Chapter 7 is not the choice since you would probably lose your home.