“Say, I am your sign. Just as I have done, so will it be done to them. They will go into exile, into captivity. And the prince who is among them will bear on his shoulder in the dark, and will go out. They will dig through the wall to carry out by it. He will cover his face because he will not see the ground with his eyes.”
What Ezekiel had acted out was a sign, a guarantee from God of would happen to both prince and people. Kings did not usually bear heavy burdens. But Zedekiah would, for he would have been brought down to a humble level by what was happening. Bearing the burdens may well have been part of his disguise. And they would go out ‘in the dark'. Compare John 13:30. It would be both literally true, and spiritually true. The future was dark before them. Their proud boast of being the chosen of Yahweh (Ezekiel 11:15) would have collapsed.
As mentioned above the covering of the face probably primarily indicated that he could not bear to look at the sacred ground which he was having to leave behind him, a measure of his despair. He and his followers would be leaving with broken hearts (compare 1 Samuel 28:14). But it may also have indicated some measure of disguise (so LXX), or even have included that he would shortly be blinded (Ezekiel 12:13).
Breaking through the wall indicated the extremity they would have come to. It was an ignominious flight. The gates would be heavily guarded by the enemy. See 2 Kings 25:4-6; Jeremiah 39:4-5; Jeremiah 52:7-8 for its fulfilment.