Making a play on a runner who reaches and passes first base...

[sleebo]

I had an interesting question posed to me at the ballpark this weekend and I didn't know how to answer it, so I figured somebody here could help...
The situation is this: Batter-runner is walked and goes to first base and jogs through the base, touching it and taking more steps down the line. Can a play be made on this runner? What is the difference (if any) between this situation and an infield single where the batter-runner runs through the base, turns and heads back to first? Can a play only be made on this infield single batter runner if he turns left (towards second base)? Thanks for your help.