I live about an hour from SBTS in Louisville, was a student there, and have known several PHD (&DMIN) students there. Here's a breakdown of common scenarios: (initials to help me remember people, but keep their identities secret):
(All these are married Family men
M-Was already a Pastor in the area, Decided to go for the degree, had a family friend who offered to help pay for part of it. Attended Seminars
J- Pastors a church in Texas...Flies to Lville a few times a year for Seminars & on-campus research work. (Apparently his church salary can cover this).
C,G, C, D, T & most others: It seems the most normal thing to happen is that a person will move to the Louisville area (anywhere within 60-80 mins away) and find a Church to pastor, or be on pastoral staff. This gives them the necessary proximity and a steady income (sometimes their spouses work too,not always).
But most importantly...A church Job is usually much more flexible than a secular job in allowing them to take random days/weeks off to go to the seminary. And they can to use Coarsework/dissertation studies in their preaching & teaching, which can ease the workload a bit.
How they pay for it? I don't know for sure...I do know of one church in the greater Louisville area that has less than 200 average attendance, and pays the pastor 90k+ a year, but I don't think that is the norm.
Most of these churches are not that big (75-300), so They Generally stay in these churches for 3-5,6,7 years, then begin looking around once their Degree is done. For many SBC churches in my area, our 7-year pastor (Who as far as I can tell, plans to stay here 20-30 more years) is one of the longest tenured pastors...So many can say this is not a good model, but I suppose it is part of being so close to a major Seminary.
Hope this helps...you can PM me if you want more info.