بسم الله الرحمن الرحيم
If it is true and genuine that the husband did not give any written or verbal talaq to his wife as well as he did not sign any paper related to the talaq and no khula took place between them, then in this case no talaq took place.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.