The stator cover (flywheel cover to use the term the CL guy used) can get whacked by the chain if the chain gets too loose and skips a tooth on the front sprocket. Typically, the damage is contained to just the stator cover. It is very easy to replace. There are just a few bolts around the perimeter of the cover to remove and a couple electrical connections. This is a VERY common place for them to get damaged. Be careful of any replacement stator covers you buy on e-bay. If they don't give you a good picture of the area that gets damaged (the area just in front of the sprocket) assume it is also damaged.
If the chain skip was more severe, it can start to get into the crankcase in the same area (where the stator cover mates to it). If the crankcase is damaged, your options to fix it get more complicated and possibly less reliable.
On a side note: if you get this machine and regardless of what you do to fix the oil leak, BUY A CASE SAVER! This is a stamped piece of steel that bolts in place between the front sprocket and the crankcase. It helps prevent the chain from whacking the crankcase / stator cover in case of a chain jump, and if it does jump it minimized the damage. Case savers are discontinued, but a perfect reproduction is available from 3WW member tapper190 (he also sells them on e-bay). If you love your 350x, you need to run it with a case saver.
EDIT: I forgot to mention, if the damage to the stator cover isn't too sever, you can get out the JB weld and build the area back up, and then carefully file it smooth and flat. I did that on my 1st 350x stator cover and it worked very well (until I bought a solid replacement cover).
- Frank
1984 200ES Big Red
1985 350X (x2)
1986 350X
1986 250SX
1984 Auto-X
1984 ATC70
1985 ATC70