If the owner of the house decides to offer a discount to market-based rent, that's going to depend on their overall assessment of the situation, and income change doesn't necessarily change anything about the situation (although it might, and probably would in this case.) Suppose one of the couple didn't have a change in base income, but did receive a huge inheritance. Then what?

Ordinarily if you rent, you don't take the landlord's income into consideration in terms of what you are willing to pay.