When a player makes a deposit in a casino, they should know that they will play against the odds, and there is always the risk of losing that money. If someone fears losing money, they should not deposit in a casino. But that does not mean they will gamble irresponsibly once they make a deposit. I won't continue to place risky bets even though I know I can lose the deposit.
If you consider responsibility in gambling, then yes, you should fear losing money. Otherwise, you will end up placing irresponsible, risky bets, which will end up losing your money. So it is kind of yes and no at the same time.
Depositing money into a casino means you are going to lose more money. This process is such that if your attitude is limited to gambling, you may not be able to do so in the future. No matter what happens, you cannot gamble responsibly if there is money left in the casino. To protect yourself from the risk of losing money, you should limit your allocation and each time you send the casino the amount of money that is within your limits and the amount that you can afford to lose. If we consider responsibility in the game, the amount of bets should be reduced in a sophisticated way so that you can keep yourself busy with other important earning activities. The fear of losing money that you mentioned is a tendency that is significantly present in every gambler/betting. The mindset should be set in such a way that you can consider every possible case for fun.