I think it is safe to say that if the language remain alive long enough, it'd be a matter of time until a character is fitted to a spoken word. Even if it didn't originally start with one (i.e., European or certain Japanese loanwords in Taiwanese), or if the original had been lost. This seems to be typically achieved by:
- Choosing a character with a similar sound or meaning in Standard Mandarin.
- Choosing a character that has the same pronunciation in the dialect/language.
- Make up a new character.
Which, given the lack of a unified authority for most such languages, means there's probably a ton of dialectal words that have been written in different ways. And that's compounded by the enormity of the existing range of Chinese characters. On the other hand, that's less that a word couldn't be written properly, and much more the result of an intense marginalisation of these dialects and languages in the past century.
(The below is taken from my answer to the thread in the Chinese Stack Exchange)
There's a few Taiwanese words where the proper Chinese character was unknown or disputed or perhaps non-existent. This, combined with long term marginalisation of Taiwanese as a respectable medium of communication, resulted in a bit of chaos. On the other hand, in 2009 the government made an effort to standardise the writing system, so there's now a designated official characters for the more common words at least.
Anyway, here are some words that apparently had no universally agreed upon correct character (prior to 2009, at least):
bē/buē
: officially 袂, was/is written as 𣍐, 未, indicating a negative
gâu
: officially , was/is written as 賢, 爻, meaning "skilled at"
buaih
: officially 勿愛 squished together, was/is written as 無愛, 覅, meaning "dislike"
suí
: officially 媠, was/is written as 美, 水, meaning "beautiful"
tsia̍h
: officially 食, was/is written as 噍, 吃, meaning "to eat"
phah
: officially 拍, was/is written as 打, 扑, meaning "to pat, slap"
beh/bueh
: officially 欲, was/is written as 要, 卜, meaning "to want"
kah
: officially 佮, was/is written as 及, 甲, 合, meaning "together, with"
m̄
: officially 毋, was/is written as 不, 呣, 唔, indicating a negative
tshù
: officially 厝, was/is written as 茨、戍, meaning "house".