Interestingly, foxes are mentioned at least 3 times in the gospels (although 2 of those instances may be from the same event). That seems quite a lot for such an animal, so Christians should take note of its importance in the teaching of Christ.
Since the Deity cares about His creation and His animals (Job 39-41, Matthew 5:45, Matthew 10:29, Psalm 147:9, Luke 12:24), He also cares about foxes. Spirits of foxes possibly may become disembodied (Ecclesiastes 3:21) (especially in such situations as a death of a fox's physical body). The Deity feeds foxes also and gives them their portion(s) (Psalm 63:10). Psalm 63:9-10 says that when those enemies fall in the low(est) of the earth (perhaps just/right above Sheol/Shaul), those enemies become a portion of foxes (although the Hebrew is spelled as "handfuls", which means what?). So foxes can be very low, perhaps even in the lowest parts of THE earth, however probably still above Sheol.
If this idea is accurate, this gives a lot of insight into the Messiah's teaching, that was important as it was recounted by two different authors, so twice: Matthew 8:20 and Luke 9:58. It seems like a random animal to talk about and associate with flying things of the heaven and their nests... unless foxes are understood more in the former manner. If fox animalians, like fox spirits / "directions", are sometimes in the lowest or LOWER parts of the earth (and therefore lower/lowest perhaps of creation), then they contrast well with the flying things of the heaven that are sometimes (and make (temporary) dwelling) in the HIGHER or highest parts of creation. One type of entity, a fox, has access to very low places, and the other type, a flying thing of the heaven, to very high places. So the choice of animal / animalian of which to speak in those verses is much more understandable.
And this may give insight about "laying down ones head" in various places, especially regarding elevation/height/depth.
The other reference to foxes in the Gospels is in Luke 13:32. Some pharisees tell the Christ that Herod wants to kill Him. Instead of mentioning Herod, Christ tells them to send a message to "the fox that" (Greek) indicating with the article THE that it might be some kind of leader of fox-spirits. Perhaps Christ spoke about a fox-spirit that was like a demon possessing Herod. This would make sense since Herod, as a human, didn't seem to have a reason to kill the Christ. Herod would have benefited more to keep Christ alive, to heal him or his family or friends if they became injured or sick, to talk with Christ out of curiosity, to see His miracles being performed to be entertained. There are many reasons Herod should have wanted to keep Christ alive, but a fox-demon possessing Herod may have had other desires to want to kill Christ.
In Asian lore, foxes had spiritual legends associated with them. You might read wikipedia article(s) about "kitsune", especially regarding spiritual possession. (And articles regarding "kitsunebi" and any other ghost-lights, will-o-wisps, orbs, and ball lightning. These phenomena are likely related to what were seen in the book "UFO of God".)
Egyptian lore has a jackal/fox-esque character that is associated with taking people from surface to underworld, like going from surface of earth, to lower/lowest of earth. Is this like foxes going up from and down to dens? It is described as having a black head and jackal-like (similar to fox- like) features. It is mentioned that that character is not the lowest or Egypt's version of Sheol / Shaul, but is slightly above it. Maybe it became a "god" of Egypt (Exodus 12:12, Isaiah 19:1, Jeremiah 46:25) if it was a kind of fox-spirit and/or jackal-spirit that tricked the Egyptians into worshiping it (1 Corinthians 10:20, Revelation 9:20, Leviticus 17:7, Deuteronomy 32:17, 2 Chronicles 11:15, Psalm 106:37, Matthew 4:9, Luke 4:7, 1 Timothy 4:1), and the other "gods" of Egypt might have done similarly, perhaps also them being other animalian or animal spirits, having the appearance of those animals in Egyptian artworks.
Interestingly, Moses' staff was associated with a serpentine entity, as it became one in some situations. If some staffs could be associated with animals and perhaps then to animalians and animal spirits, then could a fox be associated to a staff, as in a similar way that Moses' staff was related to a serpentine animalian or spirit? In Asian lore, a fox-spirit's tail(s) was/were usually related to its power and wisdom. I read that their tails could even cause fire. Funnily enough, in the bible, fire-lighting happened directly from a foxes tail, when Samson tied torches to foxes' tails and let them run through a field.
An end or tail of a staff of a mysterious character caused a fire in the Bible. If there are only 2 far ends of most staffs, and staffs are carried vertically, then wouldn't one end be like a staff's head and the other like that staff's tail? Obviously Moses' staff seemed to have a tail, as one end was seeming to correspond to the serpent's tail. In Judges 6:21, a messenger/angel from the true Deity, lit a fire using the end of his staff (in Hebrew this is not the exact word for "tail" although it can mean extremity/end).
In the Samson story mentioned above, tail of foxes are noted in Judges 15:4.