I am now rejoicing in my sufferings for your sake, and in my flesh I am completing what is lacking in Christ's afflictions for the sake of his body, that is, the church. (Col 1:24, NRSV)
Commenting on this verse, Larry Hurtado wrote the following:
Paul’s sufferings are pictured strikingly as allowing him to complete in his own flesh what is lacking in Christ’s afflictions for the sake of the church. In the preceding verses (1:15-23), Christ’s preeminence over all creation, and the universal scope of this redemptive work, are celebrated; and this reconciliation is specifically described as accomplished through Christ’s own fleshy body in his death (v. 22). As commentators rightly note, behind the reference to completing what is “lacking” in Christ’s afflictions probably lies the idea of an eschatological quota of sufferings (messianic “woes”) that must be completed so that the final consummation of God’s redemptive plan might take place. That is, the idea here is not that Paul’s sufferings compensate for an insufficiency in Christ’s sufferings, or that Paul’s sufferings contribute to the redemption of the church. Instead, the things that Paul suffered are pictured here as affording him the chance, on behalf of the church, to make a special contribution to the eschatological measure/quota of eschatological sufferings. Yet it should be clear also that the traditional apocalyptic idea of eschatological sufferings has been reshaped here by the crucifixion of Jesus, so that Paul and other believers can undergo their sufferings as service to the crucified Jesus. We may also note Philippians 1:29, where Paul reminds his readers that it has been given them (by God) both to believe in Christ and also “to suffer for his sake,” and Philippians 3:10, where Paul expresses his deep and continuing aspiration “to know him [Christ] and the power of his resurrection and the participating/sharing of his sufferings [κοινωνίαν [παθημάτων αὐτοῦ], being conformed [συμμορφιζόμενος] to his death.” (Larry Hurtado, "Jesus' Death as Paradigmatic In the New Testament" in Ancient Jewish Monotheism and Early Christian Devotion: The Context and Character of Christological Faith [Waco, Tax.: Baylor University Press, 2017], 351-71, here, pp. 365-66)
Hurtado is correct in stating that Paul is not speaking of the (eschatological) salvation of the Church, but Paul is clearly teaching a form of participatory atonement. Morna Hooker noted the following about this often puzzling passage:
Colossians 1:24 provides an interesting example of the way in which commentators have allowed their theological convictions to influence their interpretation of the text. The belief that Christ’s death is decisive and once-for-all has led some of them to shy away from the straight-forward meaning of the words. Another example of this can be seen in the refusal to allow that Paul ever speaks of imitating Christ. Colossians 1:24 reflects the conviction that we have found elsewhere in Paul’s writings, that it is necessary for the Christian to share in the sufferings of Christ and that this participation in suffering can be of benefit to other members of the Christian community. This necessity is not based on the idea that there is a set quota of messianic sufferings that need to be completed. Rather it arises from the representative character of Christ’s death. If Christ died for all, this means not only that all have died, but that they must continue to work out the meaning of dying with Christ. The acceptance of Jesus as Messiah means a willingness to share his experiences. In this sense, at least, the sufferings of Christ are no substitute for ours, but a pattern to which we need to be conformed.
The tendency to stress the belief that Christ’s death was a substitute for ours to the exclusion of the Pauline conviction that Christians must participate in the suffering of Christ is perhaps a very early one. The Corinthians, e.g., seem to have been unable to grasp the idea that there was any place for suffering and humiliation. In their calling: for them, resurrection with Christ was a past event, and this meant that they shared already in his glory, fullness, and riches (cf. 1 Corinthians 4:8). Christ had suffered—and they experienced the resulting glory. He had become for them the substitute for humiliation and death. They failed to see the necessity to share his sufferings. (Morna D. Hooker, “Interchange and Suffering,” in Suffering and Martyrdom in the New Testament, eds. William Horbury and Brian McNeil [Cambridge: Cambridge University Press, 1981], pp. 70-83, here, p.82, emphasis added).