Two modes, two answers on custody. A plain ladder mints each band straight to your wallet and the builder holds nothing afterwards. An auto-settle ladder is held by the settle contract instead — that is what lets anyone close a filled band for you — and you can withdraw it back at any time. Every contract here has no owner, no pause and no upgrade path.
No promises. A ladder only fills if the market price moves into it, and nothing here can promise that it will. A pool with no trading volume will not fill one at all.