There were a bunch of feature phones around 2014 that had an unauthorized (and poorly working) WhatsApp client. Signal of today is a bit trickier to run than WhatsApp of 2014, but it could be done. WhatsApp also ran officially on Nokia Series 40, which was a feature phone platform with apps.

There's also KaiOS which is running on phones marketted as feature phones, although it's a fork of FirefoxOS which is Android base plus an HTML+js app model (or something).