This text has always struck me as a little odd.
NASB: “Do not participate in the unfruitful deeds of darkness, but instead even expose them; for it is disgraceful even to speak of the things which are done by them in secret.”
UBS4: “καὶ μὴ συγκοινςεῖτε τοῖς ἔργοις τοῖς ἀκάρποις τοῦ σκότους μᾶλλον δὲ καὶ ἐλέγχετε. τὰ γὰρ κρυφῇ γινόμενα ὑπ’ αὐτῶν αἰσχρόν ἐστιν καὶ λέγειν.”
How is it that we’re suppose to “expose them” while not being disgraced by speaking about them? Hoehner chimes in:
The question needs to be asked: “Whose deeds are to be exposed?” It is all to easy to conclude that it is the deeds of those in darkness. Nevertheless, it is more likely that it refers to believers who are participating in unfruitful works of darkness. First, the context is speaking about believers. Second, Paul exhorts believers (not the world) not to participate in the works of darkness but rather to do the works or fruit of light. Thus, it appears that some believers were participating in the works of darkness, making the enjoined necessary. Third, in the NT there is no reprimand of those in the world. Rather, Paul exposes, rebukes, and disciplines those in the church (cf. also Matt 18:15-17). He explicitly states that believers are to judge those inside the church and not to judge those outside the church because God alone is going to judge the latter (1 Cor 5:12-13). Furthermore, instruction in Proverbs (9:7; 15:12) and even in Qumran literature (1QS 9:16) warn against rebuking unbelievers. Hence believers, rather than participating in evil works, are to help those who have fallen by exposing their unfruitful works and showing them that participation in those works is totally inconsistent with light. In this respect, the Corinthians failed to expose the sin of incest that was practiced by one of the believers in the church. It is interesting to note that the same commentators who think this exposure has reference to unbelievers also suggest that Paul was not referring to verbal exposure but rather exposure by example, that i, by maintaining a contrastive lifestyle that consists of deeds of light. [FOOTNOTE 1: Schnakcenburg, 226; Lincoln, 330] However, as stated above, the word ἐλέγχω includes both exposure and reproof. Thus the verbal aspect must be included. This idea is exemplified in other NT passages. For example, Matt 18:15-17 states that a brother is to go to the sinning brother and point out his fault. This is also true in 1 Cor 5. It is difficult to imagine Paul telling the Corinthians to remain silent, just live a good lifestyle and evil will disappear. No, to expose evil deeds includes verbal rebuke. In light of this, it is clear that it is the deeds of believers which are in question. The present context supports this with μᾶλλον δὲ plus καὶ, for not only are they not to participate in the works of darkness “but instead even” expose them. 
Of course, this doesn’t really answer the question. Even if it is the believers’ shameful works, how are we to expose them without falling into disgraceful talk? Again, Hoehner answers (I took the liberty of redacting the Greek text from the quote.):
The preposition “by” denotes agency and the object of the preposition “them” refers to those who are doing the unfruitful works of darkness. This personal pronoun does not refer back to the works of verse 11 because this would make no sense. Rather, it refers back to the personal pronoun in verse 7 where it reads “do not become fellow participants with them,” that is, those on whom the wrath of God comes. At one time believers were like those who are in darkness (v. 8). This is consistent with what is discussed above where Paul states that believers are not to be fellow participants with unbelievers (v. 7) nor participate in the unfruitful works of darkness (v. 11) done by them in secret which are shameful even to mention (v. 12).
This is a really an intriguing argument and it explains the conflict. But leaping from v. 11 back to v. 7 to find the pronoun still bothers me. The only reason to do that, as Hoehner points out, is because referring to “unfruitful deeds of darkness” (v. 11) “would not make sense” –which is exactly the observation that started this search in the first place. Still, I’m not convinced. Not yet, anyway. I guess more study is needed.
 Hoehner, Harold W., Ephesians: An Exegetical Commentary. 2007. PP 679-80.
 Ibid., 681