Regarding escrowing your rent, check with an attorney.
However . . . .
If you're still receiving housing--the housing that's specified in your lease agreement--then you should still be paying rent. What your landlord does with your payment is between him and his mortgage company. I understand your concern--and I'll get to another point in a moment--but right now you probably have a valid lease. Check with an attorney. But, as noted, if you're getting what he agreed to provide--housing--then you're obligated to pay for that service. And read your lease. I doubt that there's an "out" if the owner encounters financial difficulty. If it is, then follow the procedures you agreed to. Otherwise . . .
Now, one problem does involve your security deposit. Assuming you live up to the terms of your lease, at the end of it (assuming your lease so provides) you'd be entitled to the return of your security deposit. However, as a practical matter, if your landlord is going into foreclosure it's unlikely (possible but unlikely) that he'll be in a position to return your security deposit.
Dp2's suggestions are good. Discuss this with the landlord. Be frank. On the other hand, recognize that he's not trying to rip you off. He's got a lot more problems than you probably do. So, see what you can work out. And as Dp2 also suggests, maybe there's some way you can purchase the property. I wouldn't suggest a lease-option as the first choice. Try what's called a "subject to." The owner would deed the property to you. You, in turn, would make up any deficiencies or arrearages. You'd then promise to pay the monthly mortgage due to the lender. The mortgage would still be in the owner's name, but you'd be paying it. At some point in the future, you'd refinance, getting a new mortgage in your name.
The two issues from your standpoint are: (1) do you have enough cash to make up the owner's arrearages? And (2) Can you afford the monthly mortgage? If you do, then you could solve the landlord's problems and yours.
Hope that helps.