Following syncope of unstressed short vowels inherited from Proto-Germanic, which in North Germanic occurred in several stages between the 6th and 9th centuries, something interesting happened to words containing -i- or -j- in the root or stem1: where -j- was found at the very end of words, it was lost in Old Norse, but where followed by a vowel, it persisted.
This meant that words would now have -j- in certain declensions and lack it in others. An example of such a word is ON Frigg (< Proto-Norse *Friggju2), with genitive Friggjar (< P-N *Friggjōʀ). Here the loss of -u in the nominative has led to the loss of -j-.
Even more interesting is that this “j-before-vowels” rule applies across word-boundaries. One example is styrj-ǫld ‘Cleasby-Vigfússon: stir-age; war, fray, tumult’, a compound consisting of styrr ‘Cleasby-Vigfússon: stir’ (< P-N *sturiʀ, with genitive styrjar < P-N *sturjōʀ) and ǫld ‘age’. Here the -i/j-, which was part of the stem in P-N, but dropped out in ON due to syncope, reappears in the first element of the compound.
Another obscure-but-fun instance where lost -i/j- reappears is in the negative imperative of weak class 1 verbs. Negative imperative? A little-known thing in Old Norse is the negative verbal suffix -a(t), which just serves to negate the meaning of the verb; thus vas ‘was’ > vas-a(t) ‘was not’. Its etymology is not clear, but it’s fun to use, and very common in poetry. It has no descendants in any modern language.
There are numerous examples, most of them from the Poetic Edda, of this suffix causing -i/j- to reappear. So in st. 135 of the Háva-mǫ́l:
Gęst þú né gęyj-a · né á grind hrę́kir; get þú vǫ́-luðum vęl. ‘Bark not at the guest, nor spit at the gate; furnish the impoverished well.’
Here gęy ‘bark!’ (< P-N *gawi), imperative of gęyja (< P-N *gawjan) becomes gęyj-a with the negative suffix. Of course you may doubt this example, since -ęy- is a diphthong, and the -j- could easily have been inserted. Luckily there are other examples.
From the Vǫlundar-kviða, where kvęl ‘torture!’ (< P-N *kwali), imperative of kvęlja (< P-N *kwaljan) becomes kvęlj-at:
at þú kvęlj-at · kvǫ́n Vǫlundar né brúði minni · at bana verðir ‘that thou not torture Wayland’s wife, nor become the slayer of my bride’
I’m not sure if the phenomenon described in this article can be described as sandhi. At the very least there is in a few Old Norse words an implicit/morphologically present -j, which is dropped unless followed by a vowel. I have never seen it mentioned3, probably because it’s very rare. But, it is fun to beat people with the rule that the negative imperative of kvęlja is kvęlj-at, not *kvęl-at.
To shortly explain this terminology: the Proto-Germanic noun *wulfaz ‘wolf’ contains the root *wulf- and the stem -a- (and the case-ending -z), making it a so-called “a-stem” nominal.
Further from Proto-Germanic *Frijjō, by two sound changes: (1) -ō > -u, shared with West Germanic (cf. Old English laþu < PGmc *laþō), (2) Holtzmann’s law: *-jj- > -ggj-.
Some signs of life: the great Finnur Jónsson certainly knew of this rule, since he reverted the Codex Regius’ grem þú eigi ‘anger not’, to *gręmj-at ‘id.’ in his edition of Lokasenna 12. I know this because I was going to use it as an example in this post, until I realised it had no manuscript support.