How to get an analog camera to work with an PoE NVR?

I have 16 cameras. 8 are Foscam IP cameras and they all plug into a network switch and then I run a cat5 wire from that switch to my Westshine hybrid NVR and 8 cameras are analog BNC cable connected to that Westshine hybrid NVR/DVR so that i can also see the IP cameras.

My Westshine DVR is starting to fail it is getting old now. So in doing some eBay searches I’m now starting to see tons of PoE IP type NVR units. So I really do not want to or even need to change out the analog cameras they are about a year old, but being it is hard now to find a NVR that cannot only see my analog BNC cameras and my IP cameras thru the network switch, I’m wondering if they have some type of unit that I can plug the BNC cable into at the DVR location and then use a short PC of cat5 wire to the connect that device into the new PoE type NVR units.

And if so being I’m not familiar at all with the new PoE NVR units would need to then get a 16 channel NVR or might I be able to get a 8 ch NVR and then have the NVR see the IP cameras that are now connected to my network switch and plug that into a 8 channel PoE NVR and be able to see all 16 cameras?