When will the 4.3 branch become EOL

It is EOL. WordPress will backport security fixes when it can, but makes no promises for updates for anything except the latest version. You should have updated 3 years ago.

WordPress will be backported security updates when possible, but there are no guarantee and no timeframe for older releases. There are no fixed period of support nor Long Term Support (LTS) version such as Ubuntu’s. None of these are safe to use, except the latest series, which is actively maintained.

https://codex.wordpress.org/Supported_Versions