Ref. No. 2544/45-3883
In the name of Allah the most Gracious the most Merciful
The answer to your question is as follows:
It is correct to buy a car/auto with Zakat money and give it to a poor person, Zakat will be paid, and he will be able to pay off his debt by earning from the auto/car.
And Allah knows best
Darul Ifta
Darul Uloom Waqf Deoband