I think you are getting Bitcoin confused with Ethereum. In Ethereum, you must have enough ether in the wallet to pay the fee to send tokens. Bitcoin doesn't work that way. In Bitcoin, the fee is the sum of the source UTXOs minus the amount being sent.
Wallet allows user to do adjustments for a transaction like Replace By Fee with two options if initially, the initial transaction was broadcasted to send all bitcoins (all UTXOs) in that wallet.
- Deduct a transaction value by taking a new fee (bump fee) and decrease the transaction value.
- Preserve a transaction value and with this option, it will show errod (don't have enough bitcoin to pay fee). The user will have to manually decrease the transaction value to have enough for fee or change to a first option.