I have found the following 4 patterns in the formation of [English] idioms.
L1 > transliteration > L1 [ + translations > L2, … Ln ]
Example: Biblical book of Job 19:20
Hebrew B’QoSHi (barely, hardly, with difficulty) > transliteration > Hebrew B’3or SHinai
(using 3 for the letter ayin) > Old Testament translation > (escape) by/with the skin of my teeth
I do not know if Job used this idiom or if the original source was misheard by a later scribe.
L1 > transliteration > L2 [ + translations > L3, … Ln ]
Latin sopor quies (sleep restfully, quietly) > Hebrew SPoR KeVeS > Count sheep! > Modern Hebrew LiSPoR K’VaSiM = to count sheep (plural). Compare English soporific; quiet, quiescent. If you are counting them, there must be more than one.
[ L1 > transliteration > L1 ] > transliteration + translation > L2 [ + translations > L3, …Ln ]
[ Hebrew B’RaKHa (a blessing) > transliteration > Hebrew BeRekH (knee, leg) ] >transliteration + translation > break a leg
Compare German “Hals und Beinbruch!” = break a neck and leg!
Here Hals is a metathesis of Yiddish (from Hebrew) HatSLakha = success
[ Heb PeLeTZ + k’Foo (shiver+frozen) > transliteration > Hebrew P’LiZ + KoF (brass + monkey ] > transliteration + translation > (cold enough to freeze the) BaLLS oFF a brass monkey
Because the peh is transliterated to B, this probably arrived in English via Arabic.
[L1 > transliteration > L2] > translation [+ alt/root translation] > L1 [ + translations > L3, …Ln ]
A target language source term is transliterated to a foreign language term, followed by translation of that foreign term into the target language idiom (that has the meaning of the original target language source term).
[English my secret > transliteration > Heb MiSGeReT] > translation [+ root translation] > Eng skeleton [(in the) closet]
A Google Scholar search retrieved 2 journal articles about the transliteration of Buddhist Sanskrit words/phrases to Chinese idioms: