But I also noted that should this happen, the value of those dollars would be depreciated between the time the banks close their doors, and the months later when those dollars were paid off.
Why?
Because printing money is like adding water to a cup of coffee. The more you add, the weaker the coffee. You dilute the original cup of coffee, just as new dollars "water down" the existing supply of dollars.
When this happens, foreign investors in the dollar would sell them en masse causing the value to drop 10%, 20%, 100% or more.
In other words, what used to cost you $1 before the bailout will now cost $10, $20 or $100. This is the reality of a currency devaluation, and this is nothing new. We have seen it all our lives, we just never pay it much attention since it is a "gradual" devaluation and not an overnight one.
The following photo is New York City 1908. A 2 cents hotdog now costs $2. That's 100 to 1 devaluation!
This is why you better have some of your wealth in something other than paper.