Not based on facts, and therefore wrong or not to be trusted. You use it for things people say or believe: unfounded rumours, unfounded claims, unfounded fears, unfounded accusations. The picture inside the word is a building with nothing underneath it — no foundation — so the whole thing is standing on air. It is the word of choice when you want to push back on something calmly and seriously. A company says the reports about it are 'completely unfounded'; a court finds the complaint unfounded. That formal, official flavour is real: you will meet it constantly in news, statements, and legal writing, and much less in casual talk, where people say 'that's not true' or 'there's no proof'. One thing worth noticing: 'unfounded' does not always mean the speaker was lying. A fear can be unfounded and completely sincere — you were genuinely afraid, there just turned out to be no reason. So the word attacks the evidence, not always the honesty. The common partner phrases are worth learning whole: 'completely unfounded', 'entirely unfounded', 'unfounded rumours', 'prove unfounded' (meaning it turned out to have no basis after all).