How did "perfidy" come to mean the absence of faithfulness / trust?
Perfidy is (OED):
Deceitfulness, untrustworthiness; breach of faith or of a promise; betrayal of trust; treachery.
The roots are per- and fidēs (faith)
Per- carries several senses, but generally relating to the completeness of a thing:
Forming words with the sense ‘through, in space or time; throughout, all over’
- pervade
- perambulate
- perfect
- permute
- peruse
- pervert
These words reinforce how the prefix is used to mean "a completeness of' the thing that is attached.
"Perfidy", however, does not mean 'complete faithfulness and trustworthiness'.
Why not?
Solution 1:
Ernest Weekley, An Etymological Dictionary of Modern English (1921) has this entry for perfidy:
perfidy. F. perfidie, L. perfidia, from perfidus, treacherous, from fidus, faithful, from fides, faith. For pejorative sense of per- cf. perjure.
Unfortunately, the entry for perjure—after noting a similar origin from French (perjurer) and Latin (perjurare) and observing that perjury is older in English than perjure—says only "For pejorative force of per- cf. perfidy.
But Glynnis Chantreall, The Oxford Dictionary of Word Histories (2002) takes the next step and indicates that the prefix per- could mean in Latin (and subsequently in French and English) "to ill effect." Here are Chantrell's entries for perfidy and perjury:
perfidy {late 16th century} This literary word for 'deceitfulness' came via French from Latin perfidia 'treachery', from perfidus 'treacherous', based on per- 'to ill effect' and fides 'faith'. The adjective perfidious (from Latin perfidiosus) dates from the same period.
...
perjury {late Middle English} Perjury is from Anglo-Norman French perjurie, from Latin perjurium 'false oath', from the verb perjurare, literarally 'to swear to ill effect'. This Latin verb also gave rise to late Middle English perjure originally used in the form perjured meaning 'guilty of perjury'.
So it appears that the prefix per- in Latin somehow acquired the sense of "to ill effect" in some of its compounds, and that this sense persisted through the transition to French and on into English—at least in the two words perfidy and perjury.