Can I buy just the profitable part of a failing business and leave the rest behind?

Yes, and this is one of the real advantages of structuring the deal as an asset purchase rather than buying the whole corporation through a share sale. A buyer can negotiate to acquire only the specific assets, locations, contracts, or divisions that make commercial sense, while leaving unwanted liabilities, unprofitable operations, or troubled contracts behind with the selling entity or, in a formal insolvency, with the estate.

This is common in receivership and bankruptcy sales, where a receiver or trustee is often trying to maximize recovery precisely by selling the viable parts of a business separately from the parts with little remaining value. Because of this flexibility, your purchase agreement needs to be precise about exactly which assets, contracts, and employees are, and are not, included — anything left ambiguous in a carve-out like this tends to create disputes later about what was actually bought and what was left behind.