I'm reading Matthew 5:13 differently tonight. The UBS Greek New Testament groups Matthew 5:13-16 together under the heading "Salt and Light." The NA27 does not group the verses together this way. It seems to me that verse 13 is as related to verses 11-12 as it is verses 14-16.
11 μακάριοί ἐστε ὅταν ὀνειδίσωσιν ὑμᾶς καὶ διώξωσιν καὶ εἴπωσιν πᾶν πονηρὸν καθʼ ὑμῶν [ψευδόμενοι] ἕνεκεν ἐμοῦ. 12 χαίρετε καὶ ἀγαλλιᾶσθε, ὅτι ὁ μισθὸς ὑμῶν πολὺς ἐν τοῖς οὐρανοῖς· οὕτως γὰρ ἐδίωξαν τοὺς προφήτας τοὺς πρὸ ὑμῶν. 13 Ὑμεῖς ἐστε τὸ ἅλας τῆς γῆς· ἐὰν δὲ τὸ ἅλας μωρανθῇ, ἐν τίνι ἁλισθήσεται; εἰς οὐδὲν ἰσχύει ἔτι εἰ μὴ βληθὲν ἔξω καταπατεῖσθαι ὑπὸ τῶν ἀνθρώπων.
Verses 11-12, the last "beatitude," say that when disciples of Jesus suffer persecution on account of him, they should consider themselves blessed because their reward is great in heaven.
In verse 13, Jesus says the disciples are the salt "of the earth." In light of verses 11-12, perhaps we are to read "of the earth" as a genitive of possession or a "genitive which expresses relations merely external" (Robertson, Grammar of the Greek New Testament, p 234). That is, in the eyes of the world, disciples of Jesus still belong to the world. Yet, disciples, people who resemble the beatitudes of verses 3-12, have "lost their salt." They no longer fit it. They've become "foolish" (μωρανθῇ). They are good for nothing but trampling (καταπατεῖσθαι), and should expect to be "cast out" (βληθὲν ἔξω).
In spite of the prospect of imminent suffering, Jesus calls for his disciples to let the light of their good deeds shine (verses 14-16) in order that they might turn people's hearts away for the hopeless pattern of the world and toward their father in heaven.
In the past I've read verse 13 hand-in-hand with verse 14, as a call for disciples to "stay salty" and let their light shine. Tonight, I'm hearing it more in the context of the beatitudes. Here's my paraphrase of the passage: The values of the kingdom of God (vv 3-12) are so different than those of the world that disciples of Jesus can expect to be "trampled under foot," (v 13). To the world, they are nothing but useless salt. Nevertheless, good deeds done on behalf of Jesus (ἕνεκεν ἐμοῦ) point beyond themselves. So, let your light shine (v 14-16).
Verse 13, with its theme of inevitable suffering and its metaphorical description of kingdom life, serves as a chain-link passage connecting the beatitudes to Jesus's call for his disciples to be a testimony to hope.