If money only exists in electronic form, all transactions are electronic too. This means that for money to change from person to person, both persons need to agree on the transaction.
Of course, people may resort to treats to get the other part to give the money, just like always.
But all transactions may be monitored by a central bank, and it could be a matter of reporting the incident. Futhermore, if you force everybody to report their ins and outs (which is not rare for people who pay taxes) it could be cross referenced. Which will allow the goverment to notice when somebody is reporting a false income.
So with fully eletronic money, all transaction - even small ones - would be registered. With proper regulation, everybody will have to report. For example a person will have to report like "A gift from XYZ of such ammount" and XYZ will have to report "Made a gift of such ammount to a person" (a person, that's the name :P). With this in place, even if the goverment does not care, the thieft will be paranoid.
What happens if a person dies without reporting? - That depends on the ruling, but an interesting scenario is where the transaction is reverted.
What about a criminal that coerces the victim into reporting? The report process will require special protection. It may be the case that it cannot be done online. By anymeans it has to require strong authentication.
Money will never be lost, as it exists in ethereal accounts in the central bank... unless it is lost from the central bank. There could be rumors that this has happened in the past. Or you could just put it in the law as a form of punishment - even if never made effective.
Addendum: No cash, but there is a catch! people may still rob valuable goods. It may be the case where all manufactured or sold goods have an id, and are also reported to the goverment. This means that any homebrew item, or whatever artinal or handcraft item will not be easy to sell, as it will be required to be reigstered first.
This may also create an underground barter market, where people don't use money - or some alternative form of money maybe used. Use post apocalyptic ideas of money as inspiration.
If we are requiring people to report in person, we should not expect people to remember all transactions. Instead a personal record of transactions would be kept. And people could use the same device used for any other transaction.
To access this device we need strong authentication. Something like fingerprint and DNA scans come to mind. You also have the option of having the device implanted in the person.
In order to report, people would have to go to a special installation, where they would be left alone beyond security lines - so no criminal will enter with them or be able to monitor what they do^1 - and there they can report the robbery. All normal transactions would be reported by interfacing with a machine in the place.
^1: Unless, maybe they are part of the government force. It could be the case that cameras are there to prevent damage of the equipment in the installation. I let this as your creative decision.
If there is a machine that can interface with the device used for transactions, there is the risk that some criminal organization will create a replica that will be capable of reading - and maybe editing - the entries on the device. With such machine it would be easier to steal. Although I would expect that it will require to take the victim to a particular location where the machine is located at.
I would expect that no rouge connection to the central bank for reporting can be done, not without a proper key that is. Yet, if we consider some corrupt officials may be involved, such machine may also be able to interface with the central bank - using a key provided by the corrupt officials - allowing the criminals to report the transactions as legit.