Any closed circuit security systems, ones that aren’t cloud based will come with an NVR (like a DVR) that hosts your recordings locally. Most are wired but some support wireless as well. Generally more expensive but in my opinion worth it.

My mom bought a simple setup for I think 3 or 400 dollars at Costco.

INAL but law enforcement can still request or subpoena your video if they suspect a crime has been witnessed by your cameras AFAIK. But at least you’ll know about it.