A relatively straightforward question I presume.
Also, does someone have the option to “withdraw” their money from the system? Wouldn’t that ruin the anonyminity? Does it just get spread around?
I don’t believe the “crypto-anarchist” philosophy is evolved enough to permit a factual answer to this question. Personally, I’d need a specific proposal for an alternative payment mechanism in order to be able to comment.
Old-school bartering? Coconuts? 1920’s style death rays? 
I’m just a plain-vanilla “anarchist” (AFAIK; you’re welcome to elaborate on the “crypto” part of it) but I would do the opposite of explaining how such a system “guarantees the money”.
There would not be any money. A currency system is so tied in with traditional power-over hierarchies that I can’t imagine any fashion in which one would exist in an anarchy.
It would not be a market economy.
Except that crypto-anarchism is. Perhaps a quick stroll over to wikipedia would help.
I suppose the question doesn’t really have a factual answer, but I couldn’t justify putting it in GD. Perhaps IMHO?
The closest thing I can think of to this is e-gold, but that doesn’t seem anonymous enough for true C-A. I think that a Swiss bank account may qualify.
To the titular question, I would think that so long as the money issuer was public, there would be no issue with guaranteeing the money.
For instance, if we have the eMoney company and money holders Alpha and Beta:
Alpha requests E100 from eMoney.
eMoney creates a database entry with Alpha’s crypto ID, E100, and a unique value for that account
eMoney returns the unique value to Alpha
Alpha now offers E50 from an eMoney account to Beta
Alpha gives his eMoney account ID to Beta
Beta passes Alpha’s ID, the account ID, and a request for E50 to eMoney
eMoney checks that an Alpha person exists with that account ID and has >= E50
Since that all checks out, eMoney removes E50 from Alpha and either moves it to Beta’s account, or creates an account for Beta with E50 in it
So guaranteeing the money isn’t an issue–so long as everyone knows and trusts that eMoney is a reliable company.
As to withdrawing money…well I don’t see that this would be any different than purchasing money. In modern day society, you would probably link your money to your credit card–so it would depend on how much you trust eMoney and your credit card issuer to keep your information secret. I suppose they could create a method for doing physical transactions, where you can go to eMoney and purchase money with cash–but again this would depend on your trusting eMoney not to have cameras in their office nor people following you home.
But if we were talking about an entire society where there was nothing except for eMoney… Well, I don’t know that you could remove your money from the system in any way except for giving it away. With real-life money you can at least burn your bills–but with digital money only, you would have to trash eMoney’s database.
I assume that you would start as you do in real life, that you might get some money from your parents and then later from the corporations you worked from. Just from eMoney’s perspective these would all be random transactions between various account numbers. Your parents might have received their first money through a credit card, but once your account is created from straight digital money using only your anonymous ID, there wouldn’t be any knowing how to get back to you–but the money would be guaranteed for your ID.
Ultimately, there has to be one or more entities that are trustable. Trustable to a point that you are willing to mail them your cash (or other goods or claims to services) and receive in return eMoney of some electronic sort.
However, as the concept is that everyone is anonymous, and that implies that standard entity-trustability features (such as stock reports, balance sheets, customer references, etc.) are not available, this is a big problem.
Further, since a big feature of this system is being able to cheat the government out of taxes, it seems likely that if it ever were to get going, there would be strong pressure to break these entities.
And yes, being able to withdraw cash from the system is a mandatory feature.