@jk I don't think there's a way to make that happen. Debian stable promises this, but that won't catch even every security update:
@jk My guess is It Depends®, mostly on your package manager. unattended-upgrades has a security tag. Or you could go full nerd and use a scraper on mitre, bounce it off your installed packages and install that way.
Eventually, you'll end up stuck on the most secure LTS from 8 years ago with a bunch of manually compiled libs etc and at that point you should probably have just installed BSD and been done with it. Ask me how I know...
@jk if you're using Ubuntu you can disable the “updates” repository and leave the “security” repository enabled². That's a supported configuration and will get you what you want¹.
Pick an LTS base and you'll only need to upgrade every 5 or so years.
¹: mostly. There are some things, like web browsers, that we can't reasonably backport only security fixes to.
²: I'm pretty sure you can do this from the “software sources” GUI, but I generally poke the configuration files myself.