What happens if someone in the reserves of a branch of the U.S. military decides to move far from where s/he lives? Is the military obligated to find him/her a spot close to where s/he’s moving?
No, the military is not required to find them a billet.
But it’s complicated. How bad do they want to keep the Reservists? How senior or junior are they? A heart surgeon has a better chance in getting a billet than does a ground pounder in an over manner rating.
What happens is that they are usually found a billet close to a Reserve Center where they move to, or they can move the billet to a unit close to where he/she is moving. In the National guard it gets more complicated, and frankly, each Service is unique.
I know they’re not terribly good about accommodating stuff like that… an old college roommate was in the USMC reserve as an infantryman out of Houston, and when he graduated, he was still stuck in that particular outfit- the local DFW units were all aviation or artillery, and didn’t have any infantry billets. So he had to drive 5 hours to Houston to do his reservist stuff (which was nearly 24/7 for the weekend), and then drive 5 hours back.
OTOH, another guy I knew in college had gone from active duty Army to Army National Guard, and even though his MOS was a tank crewman, he got a spot in a local NG unit as a driver of some kind without much fuss.
I was in an Air Guard unit in the Spokane area. I got a job in Portland. Fortunately, there were shuttle services performed by Air Reserve/Guard units in the Northwest. There were two of them that flew on drill weekends, Friday evenings and late Sunday afternoon. One was a C-135 tanker that flew from Fairchild AFB (near Spokane) to McChord AFB (near Tacoma WA) and back. The other was a C-141 that flew from McChord to Portland to Fairchild and back to McChord. I could catch the C-141 on Friday to Spokane, and then take the C-135 to McChord and then the C-141 to Portland on Sunday.
Didn’t always work. One time on Sunday, a bunch of active duty guys bumped us Guardsmen off the C-135 and I had to take a commercial flight back to Portland.