They work because although they lose money, they don't lose as much money as the alternative.

In other words, if you sit on your money, it might evaporate at a rate of -3%, but if you loan your money, it evaporates at a rate of -1%.

Not at all. The bank is just an intermediary between the central bank and you. There are people in NL/BE/DK who actually get/got money on their mortage, monthly, just like a mortage payment but in reverse.

edit: for example, my mortage was the monthly Euribor-rate + 0.9% margin. Euribor-rate = -0.5, I pay 0.4%. But there are people who managed to get just a 0.5% margin. They pay nothing or get money back.