In Modern English, the only word that has a final n only before a vowel is a/an:
In Middle English, there was the pair my/mine:
Also, the was then before a vowel. What these words have in common (apart from changing pronunciation depending on the following sound) is that they are determiners. As such there should be a finite number of them.
Which words in the history of English have had two forms, one before consonants and one before vowels?