I think the main concern people have with burying a fence it that it will rust and varmints will just dig under it.
I have used stainless steal wire that lasts for many years to create a dig proof area.
However, stainless steal wire is not cheap and it is likely much cheaper for you to run some electric wire a foot or so away from the bottom of the fence and at the bottom of the fence.
If you are using electric for the varmints than you can use heavy plastic or netting for the fence and bury it. Such netting or fencing will last decades. However, you will need the electric fence to keep the varmints out!
I have seen fence buried, fence extended out on the ground away from the fence line a few feet, electric wire a foot before the fence, etc.
Having raised poultry for a while and dealing with varmints, the problems I face ranging are:
1) Raccoon pulls bird through fence and eats part of bird, generally killing it.
2) Raccoon, fox, or other canine digging under fence and killing birds.
3) Varmint getting through gate into pen.
4) Varmint finding way into chicken house through window, roof, or other structural flaw.
5) Varmint getting through flight netting or other top cover for the chicken run.
I have had to remove coyote, fox, possum, weasel, raccoon, great-horned owl, etc. from my chicken pens over the many years.
Out side of domestic animals I tend to find that most varmints attack at night. I range my birds during the daylight and keep some live traps active.
The birds I loose to varmints tend to improve the overall flock. I also keep roosters for several years. Old roosters know what to watch for with hawks, etc. The will sound the alarm and everyone runs.
This also tend to attract the attention of a 120 pound dog