What is the set of languages accepted by empty stack pda?
When defining the semantics of PDAs accepting with an empty stack, we initialize the stack with a special "bottom-of-stack" symbol. This solves your difficulty.

The set of languages accepted by empty-stack PDAs is the context-free languages. It is exactly the same set of languages accepted by final-state PDAs. The picture changes when considering deterministic PDAs: final-state DPDA accept the deterministic context-free languages, whereas empty-stack DPDAs accept the prefix-free deterministic context-free languages.