Yes, a bank may do this.You have to remember, a bank is under no obligations to make loans, either generally (i.e. it could stop lending, as many banks essentially did during the height of the financial crises) or to any particular person (i.e. to anyone who is a bad risk). Since lending is voluntary on the part of banks, they may put essentially any terms and conditions on lending that they wish to. In particular, if there concern about how a loan might be repaid, the bank could require various kinds of insurance to insulate them from risk. If you don't like this condition, you don't have to borrow the money from this bank.