"A final word is demanded concerning the threat under which the perverted human situation stands .... Can we count upon it or not that this threat will not be finally executed, ... that the sick man and even the sick Christian will not die and be lost rather than be raised and delivered from the dead and live? This question belongs to eschatology, but two delimitations may be apposite in this context.
First, .... To the man who persistently tries to change the truth into untruth God does not owe eternal patience and therefore deliverance any more than He does those provisional manifestations [of His grace]. We should be denying ... that evil attempt and our own participation in it if ... we were to permit ourselves to postulate a withdrawal of that threat and in this sense to expect or maintain anapokatastasis or universal reconciliation as the goal and end of all things.
No such postulate can be made even though we appeal to the cross and resurrection of Jesus Christ. Even though theological consistency might seem to lead our thoughts and utterances most clearly in this direction, we must not arrogate to ourselves that which can be given and received only as a free gift.
Secondly, there is no good reason why we should forbid ourselves, or be forbidden, openness to the possibility that in the reality of God and man in Jesus Christ there is contained much more than we might expect and therefore the supremely unexpected withdrawal of that final threat, i.e., that in the truth of this reality there might be contained the super-abundant promise of the final deliverance of all men.
To be more explicit, there is no good reason why we should not be open to this possibility.... [in fact] we are surely commanded the more definitely to hope and pray for it as we may do already on this side of this final possibility, i.e., to hope and pray cautiously and yet distinctly that, in spite of everything which may seem quite conclusively to proclaim the opposite, His compassion should not fail, and that in accordance with His mercy which is 'new every morning' He 'will not cast off for ever' (La. 3:22f., 31)."
(Karl Barth, The Doctrine of Reconciliation 3, 477-478)
On my first read of Barth's theology I thought he was just a master at avoiding the question, but I've come to see that he simply did not want speculations about the future to crowd out what actually had to be said on the basis of Christ's revelation.
"In your hearts revere Christ as Lord. Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have." (1 Peter 3:15)Basically I think Barth wants to say that universalism is a reasonable hope in Christ, and while it can't be more than a hope, it can't be deemed unreasonable either.