Yep. We midwesterners are part of the area where the rule is "broken". It's more common in my area too. We have a lot of extremely small churches that are remnants of former communities. Places where, quite literally, the church is the only thing 'left'. In fact, one of my churches is such a thing. I serve a two point charge, the smaller church a church about 40. In the 1800's, it was a bustling town. In the early 1900's, it was a growing, well established small town with industry and a school and even a couple restaurants! Today, it's a church. That's it. That's all that's left. Our 'post office' is shared space with a neighboring post office and quite literally, this is no exaggeration, the smaller church I serve remains the very last non-residential building in that community. In fact, none of those old buildings or even the roads are around; it's all farmland. (Though way way back in some fields, some of those old buildings still hide!) While in this case it's served by a credentialed Pastor (me), some churches like it are served by assigned laypersons. I know of some churches of 3 or 5 on a Sunday served by laypersons, some who don't even get a stipend; it's entirely volunteer. I preached at one of these churches in high school. The DS herself gave me gas money (out of her own pocket), because I was working part time for minimum wage (again, high school student) and the church was over an hour away; I literally couldn't afford to do it. But for a couple of months I preached there. 4 or 5 in attendance. When there isn't another church nearby to create a multi-point charge, these become the place for a layperson to serve. Although that's not the way it's supposed to work. As a denomination, we want to have credentialed Pastor's with the authority to officiate the sacraments. We DO have a system, though, for using laypeople; and that's the circuit. An Elder (or even a Local Pastor, there's no reason why they couldn't) would be on a 'circuit' of perhaps as many as a dozen churches, with the laypersons preaching all but one or two sunday's a month, the Appointed Pastor only preaching occasionally, but offering Pastoral care and leadership to all of the churches. The Churches aren't denied the sacraments or effective Pastoral care (NOT that laypeople AREN'T effective, it's just that often they CAN'T, most laypeople serving in that role probably have a full time job of their own)
CLM is something the denomination is sort of 'phasing out', but yes, it exists. My conference (Missouri) really encourages those who are serving in that capacity to move towards Licensed Local Pastor; but many are unwilling due to the educational requirements. Our current Bishop has been pushing for, when possible, to phase these lay ministers out into other areas of ministry and replacing them with LLP's if they aren't able or willing (or just don't feel called) to become LLP's themselves.
And yes, "supply not appointed" or "assigned" is where these laypersons fill in. Only Local Pastors, Deacons, and Elders may be appointed. Lay people can not, per BOD, be appointed to a local church. The DS is the appointed Pastor of those churches and it falls under their authority to assign someone; which is why it's frequently referred to as "DS Assigned". Although in the Missouri Conference, our current Bishop also delegates the authority of appointing part-time Clergy. While, per BOD, it falls on him to appoint PT Clergy, he essentially rubberstamps it. The DS's handle part-time appointments entirely, and the Bishop gives the 'final approval'. His reasoning is that it's unfair to ask a part-time Pastor to move a great distance, many of them can't (bi-vocational) so this keeps them in their district.
