old wallet can send coin with 0 fee.
But while bitcoin core updated, at some point, the rule adopted that fee can't be 0 regardless of amount of sending coin.
So now bitcoin can't be send with 0 fee, Right?
You still can send transaction with 0 fee.
Since clients updated those aren't considered as standard anymore and therefore won't be relayed (by the majority of clients).
Still, if you manage to get your transaction to a miner and his mining software does accept/include transactions with 0 fee, it eventually will get mined.
Technically, it is possible. But since miners are profit-oriented this is less likely to happen.