A company I worked for 12 years ago was using a version of Microsoft Navision (now Microsoft Dynamics or something). They hadn't upgraded for several years. Upgrading would have meant a bunch of workstations would have needed to use newer versions of Windows beyond XP. Navision was largely unsupported (only by a consultant, not by MS) and of course the workstations were dangerously behind (yes, we were definitely on the internet). But to the users and the owner of the company, everything was working. We had very few problems...EDI was coming in and going out, packages were packed and shipped, inventory and accounting were up to date. It felt to me like things were held together with chewing gum and duct tape, and we were one hard drive failure from disaster, but from the company's bottom line, nothing was broken.
I left before they upgraded anything, and they're still in business, so I guess it worked out. But it proves that not everything has to change to continue to work.