He is taking a loan from the state to study and will pay back only half of it
Question

                I study in a western country (Germany) where the students have the possibility to get every month a special amount of money. You have to fulfil an application form and the competent persons calculate the monthly amount which you get (depends on the income of your parents, the rent and some other things). After you have finished your studies you have to pay back half of the whole amount monthly to the state without interest (it can also be less than the half), the other half of the amount you do not have to pay back. -Is it allowed to apply for such a financial support and to get money every month from the state? -Is it perhaps not allowed that half of the whole amount you do not have to pay back to the state according to the islamic rulings?.
Praise be to Allah.If the loan will be paid back without interest, then there is nothing wrong with taking it, whether it is paid back in full or half is paid back or less than half, and even if nothing at all is paid back, because this given by the state as a help and it can waive all or part of the debt. 
The basic principle concerning that is that a loan is a contract of a charitable nature in the first place, and the lender has the right not to ask for his money back, and that is mustahabb if the borrower is hard up, as Allaah says (interpretation of the meaning): “And if the debtor is in a hard time (has no money), then grant him time till it is easy for him to repay; but if you remit it by way of charity, that is better for you if you did but know” [al-Baqarah 2:280]. 
Muslim (1653) narrated that Abu Qataadah said: I heard the Messenger of Allaah (blessings and peace of Allaah be upon him) say: “Whoever would like Allaah to save him from the distress of the Day of Resurrection, let him give one who is hard up more time (to pay off his debts) or let him waive (the debt) from him (in whole or in part).” 
But if the reason for your confusion is that this state is not a Muslim state, and in this case the student is going to benefit from the wealth of the kuffaar, there is nothing wrong with this either, in sha Allaah. Accepting the gift of a mushrik is permissible. Imam al-Bukhaari included that in a chapter heading in his Saheeh: “Chapter on accepting gifts from the mushrikeen,” in which he narrated (2618) the hadeeth of ‘Abd al-Rahmaan ibn Abi Bakr (may Allaah be pleased with him) who said: We were with the Prophet (blessings and peace of Allaah be upon him), one hundred and thirty, and the Prophet (blessings and peace of Allaah be upon him) said: “ Does anyone among you have any food?” One man had a saa’ of food or the like with him, so dough was made, then a mushrik man who was very tall came with sheep that he was herding, and the Prophet (blessings and peace of be upon him) said: “A sale or a gift?” He said: No, a sale. So he bought a sheep from him and it was cooked... 
al-Haafiz Ibn Hajar (may Allaah have mercy on him) said:
This hadeeth indicates that it is permissible to accept the gift of a mushrik, because he asked him whether he would sell or give. 
And it shows to be false the opinion of those who say that a gift should be returned to an idolater but not to one of the People of the Book (i.e., a Jew or Christian), because this Bedouin was an idolater. 
See also the answer to question number 6964 and 85108. 
And Allaah knows best.