Banks usually charge you a fee for having an account. The fees to the bank are usually withdrawn automatically from your account (you may also have other automatic transfers from your account like membership fees, insurance payments and so on).
Leaving just a small sum of money in your account, may fairly quickly turn into a negative balance. A negative balance will usually cause the bank to demand a high interest rate on what you owe them. And if this is not sorted out quickly, the bank may not want you as a customer anymore and your negative balance and unpaid fees are transferred to a collection agency which has even larger fees and interest rate than the bank.
Your credit report may also be affected. As a result leaving your bank account open may be very negative and cause serious problems for you.