Does the suffix -ify have any inherent characteristics of making letters pronounced which would otherwise be silent?
Solution 1:
Your question is based on a false premise. According to Etymology online the word signify comes not from 'sign' but from the Latin 'significare' via the Old French 'signifier'. The same source gives the origin of both the noun and verb sign as the Latin word 'signum' via the Old French 'signe'. The 'gn' in 'signe' and, probably in 'signifier' would have been pronounced rather like 'niy' (I don't have the IPA symbols available) but this would have been more evident in 'signe' than in 'significare'.
English speakers must have transcribed that sound (which does not exist in English) in two ways, one emphasising the 'g' in 'signify', 'significance' and so on and the other emphasising the 'n' in 'sign'. The fact that there are syllables starting with a 'i' following the 'gn' in 'signify' and 'significance' but not in 'sign' was probably a contributing factor. The fact that 'sign' would have been used more widely by the mainly illiterate general population might also have contributed.