Well there are "universal" remote control devices that claim to work with any DVR or similar home entertainment devices: one device to control many....
As for working with any cable service you still will need the cable box from the service provider to connect to the DVR. Or a combination device via your provider that serves both functions. I.e., Service provider coax --------> Cable box --------->DVR ---------->TV.
Google "DVR cable box connection diagram" and you will find many connection options.
However, the DVR/device being connected to the service provider's incoming cable will need to be registered with the provider as a legitimate device to receive service. Otherwise you will be breaking the law.