Still trying to figure out how that will work since blockchain itself and mining is internet based. But i'm also intetrested why there are people who really believes it's possible. How? Probably a transfer from one hardware wallet to another through a link cable between two devices?
Well, there's a distinction between being able to create unsigned transactions, creating (or signing) signed transactions, broadcasting transactions and making sure those transactions are confirmed.
Once can easily create a cold storage setup, walktroughs are available for core, electrum and samurai (apparently... I haven't checked out the links in this topic). With a cold storage setup, one creates an unsigned transaction on an ONLINE machine, uses a medium to transfer said transaction to the cold storage device and sign it.
At this point, one can THEORETICALLY move the signed transaction back on a storage device and send the device to a big miner in an offline fashion... Theoretically, a miner *could* run his mining farm offline, but he'd have to have an online machine that builds a mempool and receives the latest blocks, each time a new valid block was received, the mining pool operator would have to download the block and the top 1Mb (without witness data) of his mempool onto a stick and transfer it to his offline mining pool... If he would succesfully find a header whose sha256d hash is under the current target, the operator would have to transfer the result back to the online machine to broadcast the new, valid block... So this whole setup is completely theoretically and not usable in reality. And even with this setup, the transaction would eventually have to end up in a block that's broadcasted to the network, or it would remain unconfirmed (even unknown) forever.
If you would pay somebody by creating a transaction spending unspent outputs funding your address with an airgapped setup and give this transaction to the receiver but asking him to never broadcast the transaction, the receiver would never be sure he got payed correctly, since you can always create multiple transactions spending the same unspent outputs. It's only when a transaction is included in a valid block, and this block becomes part of the blockchain, the transaction becomes immutable and the receiver is sure you cannot "steal" his funds anymore... So just sending signed transactions between hardware devices without broadcasting might be theoretically possible, but completely worthless (in bitcoin terms)