If its mandatory in the state you reside to register all weapons, It would be impossible for fraud of that magnitude to transpire. Here in PA, all firearms must be registered. Pistols, rifles, shotguns, and even crossbows. Not just for fraud, but to Inform, say the police for a burglary call, that there are firearms in the house and what types. As such they would treat the perpetrator as armed and dangerous.

Even if its not mandatory in the state you live in to register rifles, it doesnt mean you cant. If said firearm is already registered to you, it would be impossible for someone to claim it stolen. If memory serves me correct, it would be considered fraud that you can press charges against.

Hope I cleared a few things up for you