Yes. They can be repaired. There are a lot of bikes out there with loose pinion shafts that rely on the timing cover to keep them in place. It isn't perfect, but its the reality. The biggest problem with the shaft being loose is that it makes it very hard to adjust the chain properly. So with that said, the fix is to make or buy a tool to hold the pinion shaft while you work on torquing and adjusting. Not only does this help prevent damage to the pinion shaft it also holds the thing in place so that you can get an accurate adjustment.
If mine were loose enough to cause concern, I'd probably clean it all up, put some JB Weld on it and put on the timing cover until the JB Weld hardened. Making sure of course that I didn't glue my cover on. Others might recommend having it sleeved.