You are correct in that most loans were variable rate.

But what that means is a rapid uptick in interest rates would affect a different base. With fixed rate loans it is the lending institution that would likely be in trouble. They do the best they can to manage interest rate changes but the reality is that someone has to absorb the losses when there are long term loans at fixed rates and general interest rates rise. If the bank has it hedged then whoever took the other side of that hedge pays. But most likely the bank has lent a long term loan at a fixed rate and is only covered or partly covered for a short part of that time. For example on a 20 year loan the bank may be utilizing ten year money to cover it. They have a margin for some cushion in their profit margin but if rates rise rapidly they can be in trouble. Then any losses they have comes out of their capital. 

I'm no banker and someone will correct what nuances I have wrong, but basically banks lend long and cover their positions with shorter term money. There have been some banks blow up in the last few years because of rising interest rates and people not being able or willing to pay their loans back. If we had a big jump up in interest rates in a short period of time (like the 80's) you would see a LOT of bank stress. Especially banks exposed to long term fixed rate loans.

In the 80's we had a variable rate mortgage loan on a 160 we bought. Our payments went up a bunch when interest rates rose. But the loan was with Farm Credit FLB and the increase in the loan was capped. I can't remember now where the cap was set but seems like it might have been 5% above what we started out. Had it been more than that we likely would not have made it and the way it was we barely made it. Never missed a payment and we still own that land. That cap in interest saved us but also likely put a lot of strain on an already strained FLB because of people not being able to make payments. At that capped rate I presume their cost of money at that time was even higher than the high interest we were paying, although I was not involved in the organization enough to know at the time.

When money is lost somebody has to pay. It could be the borrower with higher interest rates (variable rate or balloon loan), it could be the bank, it could be the funding corporation backing the bank, if could be the hedge source of the bank (or borrower) hedged their interest costs. But somebody has to pay up for the losses, depending on how the loan was structured. If somebody can't pay, they go broke or get collateral taken away.

I'm sure there are technical errors in my explanation. Please, someone correct them. But I think I got the gist of it right.