Is the saying: "Whoever searches for the faults of people while he has a fault, people will search for his fault. And whoever searches for the faults of people while he has no fault, Allah will create a fault for him," a sound prophetic hadith?

It is not permissible to attribute these words to the Prophet (peace and blessings of Allah be upon him). However, he did warn against seeking out the faults of people and pursuing their private matters.

On the authority of Abu Barzah Al-Aslami, may Allah be pleased with him, he said: The Messenger of Allah (peace and blessings of Allah be upon him) said: "O community of those who have believed with their tongues, but in whose hearts faith has not entered! Do not backbite Muslims, nor pursue their private matters. For whoever pursues their private matters, Allah will pursue his private matters, and whoever Allah pursues his private matters, He will expose him in his own home."

And on the authority of Mu'awiyah, may Allah be pleased with him, he said: I heard the Messenger of Allah (peace and blessings of Allah be upon him) say: "Indeed, if you pursue the private matters of people, you will corrupt them, or almost corrupt them."

Al-Saffarini mentioned that some of the Salaf said: "We met a people who had no faults, then they mentioned the faults of others, so people mentioned their faults; and we met a people who had faults, but they refrained from mentioning the faults of others, so their faults were forgotten."