DOS never had an option to shut down, you just saved your work and turned off the computer. Also with Windows 3.x it was normal to just switch the PC off, without any prior shut down process.
Back in the days most software was synchronous, there were no background processes, no write cache (and read cache was optional). Once the "saving document" message was gone, it was written to disk. With floppys and early hard drives it was easy to hear anyway, when the noise stopped it was written to disk.