I'm wondering if such a thing exists in the US. This would be a fixed-rate mortgage that would always have the same term (15 or 30 years) even if you paid more than the regular payment each month. Thus, it would behave similar to an ARM in that the term would stay the same, and your monthly payment would decrease if you paid more than the minimum.

I did some web searching and it seems that this type of mortgage is available in Canada and Australia/New Zealand but I could find no information with regard to the US.

I'm attracted to this setup because it would allow the security of a low fixed rate in combination with the ability to make extra payments now (while I have a job and can afford to do so) to result in lower payments in the future, in the event I get laid off and have to take a lower paying job.

Anyone ever heard of such a thing in the US?

umm no, the benefit of a fixed rate mortgage is that extra payments will end the mortgage sooner. So paying extra will mean that you can be free and clear sooner. The interest is front loaded so that if you pay just the agreed upon sum early on you are going to pay way mopre than if you pay extra since the extra principal payment will lower your total interest paid over the life of the loan.

I can really see the benefit of a never ending loan, if you are a banker.

Ask your servicer if they will recast your mortgage. They can if they want many times.