What is the correct word for "dependee"?
Depending on the situation and relationship, "parent" and "child" work to describe the two parts of a dependent relationship. Likewise with the terms "master" and "slave".
If you really mean "the thing depended upon", then Mr Disappointment's answer (dependency) is correct.
If you mean the thing that depends on the dependency, then "dependent" ("dependant" in the UK) would work. It's the word we use to describe people who rely on others for support, so it would make sense here.