Can I get a break on the price if I agree to keep on the failing business's existing staff?

There's no legal rule requiring or preventing this — it's simply a negotiating point between you and the seller or receiver. A buyer willing to retain existing staff can reduce the practical and reputational costs of a shutdown for everyone involved, including the seller, the receiver, and the employees themselves, which can sometimes make a seller or receiver willing to accept a lower price or more favourable terms in exchange.

If you do go ahead and hire the seller's employees as part of the deal, keep in mind that ordinary employment-law principles about what obligations follow from that hiring decision, such as how you structure their new employment terms and whether their prior service is recognized, need their own careful review. That review isn't automatic just because a price adjustment was agreed to as part of the negotiation — the price break and the employment terms are two separate things that both need to be documented properly rather than left to assumption.