The automatic lead advance works like this: When the lead sleeve is retracted by any amount, it springs back to it's full length and along with that advances the lead by that amount. The way this happens in practice is as you write, the lead wears down till the sleeve rubs against the paper. Usually we write with the pencil at an angle with the paper. This angle causes the lead sleeve to retract when it rubs on the paper and then when you lift the pencil for the next stroke, the lead sleeve will spring back into position advancing the lead with it.

If you're interested in more details and how the mechanism actually works, here is a good link: https://stationery.wiki/Auto-Advance_mechanism