[Mashiro]

Nested virtualization, no matter if it is Virtualbox or a different virtualization, is usually only possible on hardware virtualized servers such as KVM, VMWare and so on. Software virtualization or containers such as OpenVZ, LXC, Docker and similar will generally not support nested virtualization. That said you can actually run QEMU inside a OpenVZ VPS but the peformance will be very poor. That is as far as it gets in terms of "is this technically possible".

The other problem is that most likely no provider will allow this. It creates trouble of various kinds so that most providers ban such things outright.

My two cents: nested virtualization is absolutely horrible and shouldn't be done. The only thing that I and most other people would accept is running containers inside virtualized servers using Docker. Docker is simply creating containers for hosted applications on the server. So nothing is being virtualized but you still get isolated applications on your VPS without the need for multiple servers.