Is it permissible to take out an interest-bearing loan from a bank to buy a home if the person is living in difficult circumstances after a relative backed out of lending to them, coupled with the difficulty of recovering a large down payment for the apartment, and the high cost of suitable rents?

Usury (riba) is absolutely forbidden and is not permissible except in cases of necessity. Necessity is defined as a situation where an individual reaches a point that, if they do not consume what is forbidden, they will perish or be close to perishing, such that if they remain hungry or naked, they will die, or one of their limbs will be damaged. This permits consuming what is forbidden. As for need, it does not permit what is forbidden. Borrowing with usury is forbidden, and its sin is not lifted unless there is a necessity. It is also forbidden for a Muslim to deal with usurious banks if an Islamic alternative exists. A Muslim must fear Allah and seek out what is lawful, for whoever fears Allah, He will provide a way out for him and sustain him from where he does not expect.