@stuffisthings So, okay, I am a lay Catholic person, which means that I am not affiliated with a religious order. I was not sent to seminary via a parish, so there was never any investment of my church (as a whole) but there are people in my home church who are awesome and very supportive. Religious men and women (like, sisters, brothers, priests, nuns) are sent to seminary by their order, church, or diocese for specific formation. Often, they are already placed within a parish, school, or other ministry. Their job decisions are made in conjunction with their superiors. (This is as far as I know, not being a woman religious myself.) For lay students, it's a bit different. Some of us come from professional backgrounds and so do seminary and theological formation as an added thing to what we already do. A few of my fellow classmates had been teachers in parochial schools already, but decided to further their education. Once done with their degrees, they returned to teaching. Other people do this as preparation to a second career. Some of us come to seminary not really knowing what to expect but feeling called to it anyhow. Ministry work at parishes usually doesn't pay super well, but it pays just enough. It really depends on what sort of area you live, what the socioeconomic situation of your parish is, and if you are working solely for ministry or also for the church as a staff person. Some people don't even work at churches or schools - these people usually fall back on their previous skills and do something wonderful and completely different, like organizing, or working for non-profits. This comment has now gotten too long, but I hope that answers some of your questions. (oh, I don't know how it is for other denominations, but I have met a few UU ministers who are sponsored specifically by a church with the expectation that they are to return to their former position or something like it.)
Although it is possible to be placed within your existing parish, it doesn't normally work out that way. I would explain further but I am on the train right now and posting from my mobile is the worst.
I was recommended for my first job, then got recruited by another place because of that job. My post-college jobs have all been cold-application type; however, because I've been in school for such a long time, I've not had a full time job. (It's the saddest admission.) Now that I'm about to finally finish grad school, stories like this make me worried. I'm in ministry, though, so it's a lot easier to have people know about you because we are such a small community.