How does Dollar work offline? How much do you have in your pants?
Because if the world goes offline, Banks would not have all the "money" necessary to give it back to people.
If for some reason all our computers simultaneously failed without any warning, it would obviously be chaos, but at the end of the day the banks would be in a much better position to recover than anything like Bitcoin. Banks only use computer networks because they are more efficient than the alternatives; Bitcoin requires everyone to be online and does not have any alternatives. The worst thing that would happen if all computers failed simultaneously is that the banks would lose track of everyone's accounts -- a general amnesty for debtors and a big loss for people without debts -- and in the aftermath the banks would just start from scratch using older technologies.