Theoretically, the OG Pixel will work indefinitely until there's an irreparable software/hardware issue. Realistically? Depends on how the user takes care of it ;)
"End of Life (EOL)" doesn't mean that the device will end its life. It is just that the manufacturer (in this case, Google) will stop its support; no more security & OS updates, and the like.
If the user is adventurous enough, they can unlock the bootloader (warning: will delete all the storage) and flash custom ROM which at least extends the life a little further. (In addition, seems it's also compatible with Project Fi).
Anecdotal evidence: I'm using Nexus 5 which was released in 2013 (Android 4.0 Ice Cream Sandwich) and EOL in 2016 (Android 6.0 Marshmallow). I flashed Lineage OS after that until it's not maintained (Android 7.1.1 Nougat). As of 2019, the phone is still usable in daily life.