The messaging app Signal, which bills itself as ultra-secure, can be used via just a landline if you don’t have a mobile phone, but do have a computer and some time.
This is one of those, ‘it’s possible, but you probably won’t want to’ situations. Nonetheless, some people do opt to go entirely without a mobile phone and that’s not a reason to stay out of touch with friends, necessarily.
By hacking the Signal Chrome source on Github, he was able to successfully register an account and use the service without a smartphone, using just a landline number.
However, Reinholdsten notes that it’s not an entirely secure process, and does give away his home address and telephone number, which really doesn’t sound ideal.