The promise of Isaiah 45:22 falls within a longer argument about who can carry and who can save. The idols cannot; indeed, they themselves must be carried by beasts and cattle (46:1-2). But God can carry and will save (46:3-4).
"Carrying" becomes equivalent to "saving" in this passage. To be saved is to be carried. Throughout the Bible, God is pictured as one who carries--as an eagle (Exodus 19:4), a mother (Isaiah 66:12-13), a shepherd/warrior (40:10-11), a bearer of sin (53:12), even here in this passage as a beast of burden. God carries the people whom God governs on God's own shoulder (9:6); people and beasts must carry the idols, but God carries all.
The New Testament continues this theme with the announcement of Christ who came to "bear the sins of many" (Hebrews 9:28). German theologian Dietrich Bonhoeffer makes the same point: "God is a God who bears" (Dietrich Bonhoeffer, Discipleship [Minneapolis: Fortress, 2003] 90).
46Bel bows down, Nebo stoops,
their idols are on beasts and cattle;
these things you carry are loaded
as burdens on weary animals.
2 They stoop, they bow down together;
they cannot save the burden,
but themselves go into captivity.
3 Listen to me, O house of Jacob,
all the remnant of the house of Israel,
who have been borne by me from your birth,
carried from the womb;
4 even to your old age I am he,
even when you turn grey I will carry you.
I have made, and I will bear;
I will carry and will save.
New Revised Standard Version Bible: Anglicized Edition, copyright © 1989, 1995 National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved worldwide. http://nrsvbibles.org