Is there such a thing as a third party DVR that works with cable?

The ability to get cable signals in the clear is on the decline, and completely gone in some systems. Cable companies have converted many channels to data rather than a regular signal. Connecting the cable straight to the TV may not work for any channels at all, even the basic cable ones. I think the driving force is to allow more data to go on the coax rather than to prevent people from stealing signal. By converting a normal channel to data, they get more bandwidth on the coax for internet data. So even if you can get some channels directly on your TV, that may eventually change. It just depends on your particular cable provider and how aggressive they are with channel conversion.