A Murray's firing pin and a Kivari trigger will work wonders on an SKS.
The firing pin channel is tapered, so if anything gets stuck in there, it can cause the firing pin to get stuck forward. Then it acts like an open bolt gun, only much less safe.
Any newly acquired SKS absolutely needs to good hard cleaning on the bolt. A full break down isn't hard, once you've done it a few times. The firing pin retaining pin feels like it was pressed in, and can be difficult to get out for cleaning the firing pin channel. A good set of brass punches, a pin block and a lot of patience go a long way here.
Soaking the whole assembly in solvent works, too, if you can't get that retaining pin out.