Pretty much all personal bank accounts have a unilateral termination clause. I would be surprised to see a mortgage where the bank can't totally wreck you if they feel like it.
Anyhow, you still need a bank account to get paid. If you can only work jobs that pay you in cash and don't need any access to bank accounts or the Internet themselves, that rules out 99% of businesses that could employ you.
That is about changing an agreement. The bank can fire you as a customer, pursuant to the existing agreement, usually without specifying a reason. This has happened in the past.