What is the ruling on taking a training course and receiving its certificate for free after a student fails an exam, and the teacher rectifies the situation by granting him the course and certificate for free?

If the questioner wishes to benefit from the concession (rukhsah), he must take the course, obtain the certificate, and pay its fees. It is not permissible for him to exploit a teacher's mistake to burden him with the fees, because that is consuming wealth unjustly. Allah Almighty has prohibited consuming wealth unjustly, and the Prophet, peace and blessings be upon him, forbade taking a Muslim's wealth except with his willing consent. He also warned that whoever takes a Muslim's wealth without right will incur Allah's wrath.