This computer virus would take advantage of two technologies:
1) A p2p cryptocurrency.
2) Fully homomorphic encryption.
A p2p cryptocurrency allows cryptographic keys to be used as money - double spending that money is impossible unless you match the computational power of the entire p2p network.
For an example of a working p2p cryptocurrency see link for Bitcoin.
Fully homomorphic encryption allows the construction of programs which may be run on encryptions of their inputs to produce an encryption of their output. They can basically interact with a user without ever revealing their internal state.
This virus would store a certain amount of seed money (say $10,000) and some software inside its homomorphically encrypted container. This fact is advertised somewhere, along with a download.
A user could persuade this virus to spit out parts of the $10,000 by giving the software inside it what it wants. This could be access to CPU power, internet, the p2p currency network, or other things that it needs to spread and survive. When it copies itself, the virus rewrites itself and the stored wealth is divided between the two copies.
Some people would thus install this virus voluntarily!
As they spread, the copies would also find ways of earning money, for instance by sending spam via botnets and selling that capacity to whoever wants to pay the copies with the cryptocurrency.
Eventually a whole ecosystem could develop where viruses trade (or steal) from people (and other viruses). Using real money. If they are well written they might accumulate large amounts of money for nothing but their own benefit.
Deleting the virus copies would destroy the money. Quarantining the copies on some database would make the money unusable. This would make it extremely hard to get rid of these viruses. There is the aspect of "social infection" on top of the infection of computers alone.
As long as they are well written, the only way to "safely" get the money out of the virus copies would be breaking the cryptography.