This is a common problem with 850s. The speedometer is driven electrically, while the odometer is mechanical.
There's a tiny little gear inside the odometer that runs it from a motor; it's no longer tied directly to a speedometer cable like older models. What happens is the gear gets old and brittle and loses teeth, at which point it can no longer turn the odometer.
My wife's '96 850 had the same issue when I got it, and a little internet research turned up the answer above. There are companies that make replacement gears you can buy fairly cheaply, but it does require a fair amount of mechanical aptitude to pull the instrument panel and disassemble the speedometer assembly.
One note of caution that I learned the hard way: you have to take the front cover off the instrument panel, exposing all of the gauges. Be very careful not to disturb the position of those little needles; I ended up messing up the gas gauge, speedometer and temperature gauge, and it took a lot of trial and error to get them put back in so they showed the right readings.
If I recall correctly, I found instructions for doing the gear replacement online, but it's been so long that I don't have the web page(s) I found any more. A lot of times the manufacturer of the replacement gears have instructions on their web sites.
IPD USA sells them and has instructions.
850 Odometer Gear