It would be the student’s responsibility to get insurance to cover personal property like a coat…but like.y it would not be worth a claim as the deductible could be higher than the cost of a coat.
Time to find a friend with a car. Take a little trip to the nearest shopping places…winter coats are now on sale.
I also would suggest a resale store.
In the meantime…layers…sweater or hoodie under a fleece.