In the past 2 years, I paid the city and prefectural tax by myself because my previous company does not want to do it. Basically they just took the income tax per month and I pay the other taxes every 3 months.
If your friend is going home already , he can file the income tax return in advance.
I got this information from Nagoya's HP:
Filing Income Tax Returns
Let him try to go his/her City Tax Office and try to explain his/her situation.