Loan words borrowed from the middle/end of original word? I was thinking about 氡, radon recently. The pronunciation: dōng (dong1) seems to suggest that sound was borrowed from the ending of the English word. Wiktionary corroborates this theory:

Etymology
Borrowed from English radon.

This is quite interesting because most loanwords seem to come from the beginning of words, if anything, and especially not the middle or the end of a word. You might expect some form of: rui, for instance, for radon.
What other loan words exist where the sound was borrowed from the middle/end of the original word?
This article (p. 60-61) provided the reason 氡 (radon) is based on the latter syllable. In summary, this was the result of an argument between Chinese chemists appointed to element naming in the early 20th century. Those that argued radon should not be given a pronunciation similar to 鐳 (radium) so as to avoid confusion won. The lost faction argued  reflects the origin of radon from the alpha decay of radium better.

Wikipedia argues 砷 (arsenic) and 鋁 (aluminium) came from the second syllable of the English equivalent. 碘 (iodine) came from the third.

Another example I can think of is the Taiwanese translation of Al-Qaeda, 蓋達組織 (not a character per se). That is so because 'al-' is an Arabic definite article ('the') and Chinese does not have a grammatical equivalent, therefore omitted. However, the translation 阿爾蓋達組織 is still perfectly valid.