Let me assure you that there's no problem with the premise of the question. The issue at hand is not a debate about whether such a site exists. As hard as it is to believe, I have a need to access such a site, where dial-up Hyperterminal is the only way to remotely access the site.
When I had landline before, I simply dial-up using a modem to communicate with it on my desktop. But now with internet phone, I can still connect with the site, but the stuff transmitted through the HyperTerminal is just unreadable junk. For those of you that's been around long enough to remember the old BBS decades ago, it's like the communication between my computer and the site is at a wrong "baud rate" or speed.
I have been told that dial-up HyperTerminal is a similar technology as faxing. Unfortunately, faxing is also a problem with internet phone. Perhaps another way to think about this is to try to figure out how to get fax working on the internet phone, which may then serve as a template to solve the HyperTerminal problem.
I forgot to mention that I did think about the route of using a cell phone as a conduit. Unfortunately my cell phone is not a smart phone and I don't think it can run any applications. I had an old cell phone years ago (can't recall its brand and model) that has a built-in faxmodem, which probably could do the job by communicating with the computer via IR or bluetooth.