A few options for synonyms for "closing-out sale" might include terms like clearance sale, liquidation sale, end-of-season sale, or door-closing sale. These all generally indicate a sale where a business is looking to sell off remaining merchandise and close out a particular season or product line. Other options might include phrases like going-out-of-business sale, final clearance, or blowout sale. Ultimately, the exact phrasing used may depend on the specific context and goals of the sale, but these options all signal a sense of urgency and a great deal for customers looking to get their hands on discounted items.