What should be done if it turns out that the person who received zakat is actually wealthy?

The person obligated to pay zakat should investigate to whom they are giving zakat. If, after investigation, they conclude that the recipient is eligible to receive zakat and give it to them, but it later becomes clear that the person was not eligible, the zakat is still considered valid. If zakat is given without investigation and it later turns out that the recipient was eligible, the zakat is valid. However, if it is understood that the recipient was not eligible, the zakat is not valid and must be given again. (Ibn Abidin, Radd al-Muhtar, 2/352-353)

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu