Well, if a pistol or machine gun is lost you call local law-enforcement and then you reach out to the ATF and you tell them that FedEx or UPS lost a machine gun or pistol.
When a firearm is lost via one of the major shippers that tends to get a pretty immediate response. Especially if it’s a machine gun… in that case I’ve seen the FBI in the ATF sure but UPS in stark given them more than a ration of crap.
It seems that if a suppressor is lost they don’t really care as much. In that case you type out a letter and you sign it, then you scan it back in and then you email it along with the body of an email paraphrasing whats in the letter to the NFA branch of the ATF.
They will put the information in your NFA file and inform anybody who comes looking for those suppressors that they were stolen. Then you call up the manufacturer and tell them that your suppressor was stolen and to keep an eye out for it. If a stolen suppressor shows up at the manufacturer they will contact the ATF who will then have some words with the individual that sent it to the manufacturer.
It’s certainly legal to send a firearm / suppressor back to the manufacturer for repair directly. What I’m not really certain about is what the procedural rules are for sending a class three item directly to an FFL for repair who is not the manufacturer.
I’ve done this in the past and UPS, for example, requires a copy of the FFL the firearm or suppressor is going to.