What gives value to money? There was a time when money was pure gold. There was a time when money was a certificate that you own a quantity of gold in bank (banknotes). Now the money are just quality paper, without any deposit behind. How that it has any value?
Some said that money is just a convention, and the fact that the state accepts that coin as the "legal tender" gives it value. However, we know many coins that loosed theirs value even with the state sustaining it. How that other coins survives?
I claim that debt is the one that gives value to the today's money. Let's see why:
Let's assume that, one day, all the people suddenly decide that there is no reason to have trust in the value of a certain coin, let's name it coinX. We know that money tends to loose value based on psychological contagion. Let's say the perceived value of coinX went from it's usual value to absolute zero in only one night. No man has any trust anymore that coinX worth more than the paper that is printed on, it's a mass psychosis. What could save our coinX for sudden extinction like hundreds of coins through history?
Let's see first the case when there is no debt in that coin. People refuses to be payed in coinX and chose any other trusted coinY for selling goods and services (including work on salary). CoinX is actually dead, nothing could reverse the mass psychosis.
Let's take the case when there exists significant debt in coinX, including bills, mortgage guarantied loans and some enforced laws for debt to be payed, like jail for not paying debt. In this case, we will still have some people that are in need of coinX, even if they also think initially that coinX worth nothing. However, they will realize that if they are not able to obtain that "worthless papers", they risk loosing the mortgaged house, business bankruptcy, jail or other legal repercussions. The value of the coinX money for this people that owes coinX is not really zero, they kind of need it...
We have again 2 case. If there is plenty of coinX that is not owed to anyone, probably the debtors could obtain the coinX in exchange for something of small value (huge depreciation of coinX). On the other case, if there is a certain scarcity of coinX, people will compete in buying coinX, increasing it's value until the initial value or even a little more. Buying coinX includes accepting salary in coinX (in exchange for work), selling goods or services on coinX or exchanging another trustful coinY for coinX.
Normally, the value exchanged for coinX will not exceed the cost of not paying the debt in coinX. A loaner with a mortgaged house will tend to "buy" coinX with a value less than the current value of the house at stake. However, it's not unlikely that people would accept to "buy" coinX at a value close to the value when they contracted the loan.
The level of coinX's perceived scarcity in relation to the quantity of debt is the key for maintaining the value of coinX.
If there are plenty of coinX that does not need to be payed back to anyone, than coinX could significantly reduce his value, because the supply is higher than the demand. When people starts to realize this, they will rush to sell coinX at lower value than before. This is because, when all the loans are payed, the remaining coinX will not be needed by anyone, so they will actually value zero. There would be a spiral of depreciation for coinX.
If the perception is that the supply of available coinX is just below the total debt in coinX, then people will fight to get coinX before there will be no coinX available. In this case, coinX will keep or increase his usual value. Of course, it is a game of perception. There are debts that needs to be payed in years, the demand/supply is happening only for what is needed in the near future. There are a lot of things that could distort the perception of coinX's supply (like central bank actions).
If there are many loans in default (see "subprime" loans), the quantity of demand for coinX will be reduced. In general, nonperforming loans are not a good thing for a coin's value. However, there are still other mechanisms that a central bank has to increase the coinX's scarcity.
A coin that has many loans tends to increase it's value. The quantity of debt is a little more than the loaned value (because debt includes interest) so the demand from the debtors will increase in the the following years. Controlling the quantity of available money, this could result in increasing the value of that coin even on the short term, see CHF.
For maintaining the value of a coin, it is important to have a balance between the quantity of current debt re-pay rate and the quantity of money that are available for paying something else than debt. "No debt" would not be good for the current currency system.
A coin does not work if there is no powerful enough state that enforces the paying of debts in that coin. States that have a powerful army (like United States) are able to loan their coin and enforce the re-pay of that debt. Fortunately, most of the time, the army only need to be shown, not used. Switzerland is a special case, it uses a very soft power to enforce the repay, but I guess that maximum one country could have this special status on earth.
Bitcoin (and similar) will not fly without a significant quantity of debt denominated in that coin. Even if banks will start to borrow bitcoins, there will still be a path to pay all the debt and have some remaining bitcoins that are not needed for removing any liability. Also, a fixed volume coin is kind of deflationary and tends to make people to keep that money until it increases it's value; this is not good for a coin that have to intermediate economical exchanges of goods.
Disclaymer : I do this analysis as a hobby, I am not in any way certified to give economical advices. Use this conclusions at your own risk!