Not unless either party has the ability to walk away, which means multiple buyers. If I’m a buyer and I know you have no other options, why would I negotiate?
If one has no options and they treat the other party with an acknowledged lack of options, the poorly treated party can undermine the dominate party through publicity and peer shaming. There are many options for the individual trained in negotiation, and walking away for other options is the most primitive and least effective maximization strategy.