Better to have a relativley soft brass jagcome back thru the barrel than a steel rod. Even some coated rods can expose steel where the coating ends near the rod tip. And steel on steel is the main concern in that you may mar the rifling or more importantly, where you may may it at the muzzle crown. You can get away with a back and forth stroke as long as you don't pass out of the barrel or into the chamber where you will loose the patch. Still, with the jag on, no harm no foul, just pop the patch the rest of the way out and finish.

Those crown things are to protect the rifling at the muzzle as you pass the rod into the barrel when cleaning from that end. Not the best way to go though. And for a stop, like bigcountry said, just use your finger position as a stop so you don't pass all the way thru. If you clean a lot, or have a target or varmint/sub MOA rifle and are worried about damage to the rifleing, my advice would be to get a bore guide for cleaning from the breach. They also keep the gunk and solvents from getting into the action of the rifle.