An employment exists when an "employer" employs an "employee". During the employment the "employer" is the active person, the person who employs, and the "employee" is passive person, the person who gets employed. I am wondering if this is a general rule. Is it possible to convert a noun with an active meaning into a noun with a passive meaning be replacing the suffix "er" with "ee"?
The -ee ending is a rare example in English of a structure that picks out the experiencer of something, whether they would be the subject or the object of the related verb.
So when A employs B, B is the object of the verb "employ". They experience being employed, and we call them an employee.
But when A attends a meeting, A is the subject of the verb "attend". But they are still the experiencer and so can be called an attendee.
Similarly a legatee experiences being left something (in a will), an assignee experiences having a task or right or contract assigned to them (all objects of verbs with an actor); but a retiree is the person who retires (subject) and they experience the retirement.
(It is no accident that many of these are legal terms: until quite recently, this suffix was pretty well only used in legal contexts: this ngram shows that the non-legal terms "retiree", "invitee", "attendee" and "mentee" have all arisen since 1900, while this one shows that the legal terms "lessee", "assignee", and "legatee", though much less prevalent since 1960, still dwarf the non-legal ones. I have left employee off, because since 1900 it outstrips all the rest put together, so it makes it hard to see anything on the ngram).
The suffix has become more productive in the last few decades: retiree started appearing about 1940, attendee and tutee around 1960, mentee after 1980.
I have found one possible exception to the observation about the "experiencer": respondee seems to have had a small amount of use to mean "a person who responds (in a survey or questionnaire)", which to me seems more like an agent than an experiencer. It is listed in Wiktionary, but not the OED; and it gets only 12 hits in the WOW corpus.
A note about the linguistics: this arrangement, which picks out the experiencer whether they are the subject or the object of the verb, is part of a pattern called what is called "ergative-absolutive alignment" which is built into the verbal system of many languages, but few in Europe.
Here are a bunch of them, not all referring to people or relevant to this answer but many of them are. For example: ghee is a type of butter, but assignee and referee are functions people perform.
Sometimes, the associated noun is very far from the er/or and ee.
For example: assignment, assignee, assignor
Rather than saying active/passive, it's better to say a person performing an action (pay, payer) and the person to whom an amount is paid (payee) or on whom the action is performed. But each word with ee will have an individual meaning. A mentor is someone who helps someone in some field of endeavor and a mentee is the one helped.