Trevor T. some time ago raised an interesting question: “Why is someone who escapes called an “escapee”? Shouldn’t they be called an “escaper”? The prison, being the thing that is escaped from, should be the “escapee” I would’ve thought. Otherwise it implies that the prison has escaped from around the prisoner, rather than the prisoner from inside the prison. Does that make sense?”
The -ee is used to indicate the object of the underlying verb in noun derivations, e.g. employee “someone who is employed”, inductee “someone who is inducted”, confirmee “someone who is confirmed”. The suffix -er is usually used to mark the subject relationship: employer “someone who employs”, inductor “someone who inducts”, confirmer “someone who confirms.”
However, there is a strong tendency for English to use -ee to denote the subject of intransitive verbs (those that do not take direct objects): standee “someone who stands”, retiree “someone who retires”, waitee “someone who waits”, escape : escapee “someone who escapes”. This is because of a tendency among intransitive verbs for the subject to be the “undergoer of the action”, the same definition as the object of transitive verbs. You can’t wait someone in the sense of waitee but the person waiting undergoes the process of waiting.
So, in some sense linguists are not quite sure of, the objects of transitive verbs are semantically similar to the subjects of intransitive verbs and the distribution of -er and -ee tends to reflect the semantic rather than the syntactic differences.