Sell a 0.6-delta call, buy 0.6 shares. Small moves now leave the position roughly unchanged.
The hedge goes stale because gamma changes delta as the market moves, so hedging is a continuous process. Rehedging frequency trades transaction costs against hedge error; desks use delta bands rather than a clock.
What remains after hedging is the intended position: gamma, vega and theta - a bet on realised versus implied volatility.
The interview answer: yes, you can lose money on a perfectly delta-hedged position, because direction is not the risk you kept.