grammar - Are contractions "open"?

I'd guess contractions are closed, but it has a lot to do with how you use the term "contraction". If you mean by the term any written form using an apostrophe to suggest an unpronounced vowel, then it would be open, because in casual pronunciation, in some dialect or other, many, many vowels can be lost, and how that is represented in writing is a question of a writer's style and ingenuity. For instance, the example "How're you doing?" might more typically be written down "Howra doin'?", without any orthographic apostrophe where the missing vowel is. Personally, I would not call this "contraction", because I reserve that term for a change which is conventionalized and applies only in a fixed, enumerable list of cases.

For instance, the vowel of "are" can be omitted quite freely, and what is left is either a syllabic or a nonsyllabic "r". However, when the "r" is nonsyllabic, in the particular combination "they're", the "ey" part loses the glide part of the diphthong, so it winds up sounding just like "there". This doesn't happen except with certain pronouns, so since it is grammatically restricted, I would call this a real contraction. Similarly, "he will" when written "he'll" can lose the glide part of the diphthong, so that it comes to be pronounced just like "hill". Now, that's a contraction.