There are a number of verses in these chapters that find their fulfillment in Jesus. The most obvious one is Isaiah 28:16 which is quoted in the New Testament:
See, I am laying in Zion a foundation stone,
A tested stone,
A precious cornerstone, a sure foundation:
“One who trusts will not panic.”
In 25:8, we have words that are echoed at the end of the book of Revelation: “Then the Lord God will wipe away the tears from all faces.” Why will our tears be no more? Because “he will swallow up death forever.” Paul tells us in 1 Corinthians 15 that this is exactly what was and is and will be accomplished in Jesus.
Regarding death, C. S. Lewis writes most eloquently in his book, Miracles,
On the one hand Death is the triumph of Satan, the punishment of the Fall, and the last enemy. Christ shed tears at the grave of Lazarus and sweated blood in Gethsemane: the Live of Lives that was in Him detested this penal obscenity not less than we do, but more. On the other hand, only he who loses his life will save it. We are baptised into the death of Christ, and it is the remedy for the Fall. Death is, in fact, what some modern people call “ambivalent.” It is Satan’s great weapon and also God’s great weapon: it is holy and unholy; our supreme disgrace and our only hope; the thing Christ came to conquer and the means by which He conquered.
However, death is not the end, certainly not in the New Testament, nor even here in Isaiah. The prophet strikes, perhaps for the first time, a new note:
Your dead shall live, their corpses shall rise.
O dwellers in the dust, awake and sing for joy!
For your dew is a radiant dew,
And the earth will give birth to those long dead. (26:19)
Of this, Lewis also writes in Miracles, by way of commenting on the New Testament doctrine of the Resurrection of Christ….
From the earliest times the Jews, like many other nations, had believed that man possessed a “soul” or Nephesh separable from the body, which went at death into the shadowy world called Sheol: a land of forgetfulness and imbecility where none called upon Jehovah any more, a land half unreal and melancholy like the Hades of the Greeks or the Niflheim of the Norsemen. From it shades could return and appear to the living, as Samuel’s shade had done at the command of the Witch of Endor. In much more recent times there had arisen a more cheerful belief that the righteous passed at death to “heaven.” Both doctrines are doctrines of “the immortality of the soul” as a Greek or modern Englishman understands it: and both are quite irrelevant to the story of the Resurrection. The writers look upon this event as an absolute novelty. Quite clearly they do not think they have been haunted by a ghost from Sheol, nor even that they have had a vision of a “soul” in “heaven”…. What the apostles claimed to have seen did not corroborate, nor exclude, and had indeed nothing to do with either the doctrine of “heaven” or the doctrine of Sheol. Insofar as it corroborated anything it corroborated a third Jewish belief which is quite distinct from both these. This third doctrine taught that in “the day of Jahweh” peace would be restored and world dominion given to Israel under a righteous King: and that when this happened the righteous dead, or some of them, would come back to earth—not as floating wraiths but as solid men who cast shadows in the sunlight and made a noise when they tramped the floors. “Awake and sing, ye that dwell in the dust,” said Isaiah, “And the earth shall cast out the dead” (26:19). What the apostles thought they had seen was, if not that, at any rate a lonely first instance of that: the first movement of a great wheel beginning to turn in the direction opposite to that which all men hitherto had observed. Of all the ideas entertained by man about death it is this one, and this one only, which the story of the Resurrection tends to confirm. If the story is false then it is this Hebrew myth of resurrection which begot it. If the story is true then the hint and anticipation of the truth is to be found not in popular ideas about ghosts nor in eastern doctrines of reincarnation nor in philosophical speculations about the immortality of the soul, but exclusively in the Hebrew prophecies of the return, the restoration, the great reversal. Immortality simply as immortality is irrelevant to the Christian claim.
It is this swallowing up of death, and the actuality of resurrection life that follows, which gives us hope and peace. “Those of steadfast mind you keep in peace—in peace because they trust in you.” (Isaiah 26:3)