EDIT: This probably is no longer possible as LoyceV suggests?
It's true, in fact AFAIK it's not possible since Core 0.11 releases which set default minrelaytxfee to 0.00001
BTC (aka 1 sat/byte)
I need a wallet that support sending bitcoin with 0 fee.
Older wallets can do this, but the current Bitcoin network doesn't accept it.
But it's still valid transaction if it's included on block. So it's possible if you directly connect to miner/pool nodes and it's configured to accept transaction with 0 fee, even though it's not realistic scenario.