I would know if it is possible to send BTC without a transaction fee regardless of theoretically or practicall..
It has never been happening, but i don't know if we can manage to send bitcoins without fee in the future.
Even sending coin which using Proof of Stake (PoS) algorithm, it still need fee, although only small fee.
But in cryptocurrency, you only have to pay small fee without regarding of how much you send the coins.