there are a few altcoin blockchains that have this feeless transactions. such projects usually requires the developers to host the blockchain on their own servers as other people would be hesitant to do it for free. this can be a possibility if dev team has a good amount of pre-mine by themselves. on the other side of the story, dev team can design the blockchain to give those who host some benefits like staking, which will encourage people to open their wallets online.
some web wallet servers (like coinbase) or exchange servers also offer feeless transactions between members.
right now, all i can think of about sending any coin (bitcoin or altcoins) without transaction fee is by sending the private key of the wallet to the other person. this is only possible if you have the exact amount in your wallet that you are going to send. for example, i want to send 1 btc to someone. and I have an address in my wallet that have exactly 1 btc. I will just give the other person that address' private key. the major drawback here is there would be 2 parties who would know the private keys.