Well, it looks like I might be the only Alaskan around at the moment, so I guess I should comment.
First, they're not village police; they're Village Public Safety Officers. They are not sworn law enforcement officers, and they do not have firearms training, hence they are unarmed. This has come up in state politics a number of times, increasingly so in the past five years or so. As someone mentioned earlier, the Anchorage Daily News (adn dot com) did a series of articles about this last year.
The state is having a terrible time recruiting for VPSOs. (And they recently cut the recruiting budget for the program.) Long hours, low pay, (perhaps no guns) and I'm sure the list goes on.
There is a long list of social problems in the villages. Alcohol and drug use is at the top of that list. So much so that the state is now training teachers to identify and deal with Fetal Alcohol Syndrome Disorders in the public schools. Many, if not most, rural native viullages are dry. Many, if not most, opted out of the state's marijuana legalization.
Incest and sexual abuse of children is a long standing concern. Sexual assault of native Alaskan women-even in the larger cities (often times underreported, uninvestigated or not punished - the adn just published a series on that, as well) is another long standing problem.
Unemployment in the villages is extremely high (80% or more). The primary employers out there are the federal government (USFWS, BLM, etc) and the local school districts. (Who also have a difficult retaining teachers.)