Can I negotiate the price down just because the business is already in financial trouble?

Generally yes — price is a matter of negotiation, and a seller under financial pressure often has less leverage, which naturally affects what price the market will bear. There's no rule against negotiating hard just because the seller is struggling.

The caution is on the other side of that same coin: if you're buying directly from an owner you know is heading toward insolvency, rather than through a formal, court-supervised receivership or bankruptcy sale, pushing the price down aggressively can create risk later. If the business ends up in formal insolvency proceedings afterward, a very low price paid to a seller known to be in trouble can be challenged as a transfer at undervalue or an improper preference, particularly where the buyer had some connection to the seller or clear knowledge of the seller's situation. A court-approved sale process is far more resistant to this kind of later challenge, because the price has already been tested and approved. Outside that process, keep good records showing the price reflected genuine, arm's-length negotiation rather than simply taking advantage of distress.