The excerpt I’ve used at funerals is brief:
But now, thus says the Lord, who created you, O Jacob,
and formed you, O Israel:
Fear not, for I have redeemed you;
I have called you by name: you are mine.
When you pass through the water,
I will be with you;
In the rivers you shall not drown.
When you walk through fire,
you shall not be burned;
the flames shall not consume you.
For I am the Lord, your God,
the Holy One of Israel, your savior.
The prophet is reassuring people post-Exile. Misfortune will cast doubts, but God will always redeem, and will never allow us to be consumed and destroyed.
Through the lens of Jesus Christ, the believer hears of reassurance. We will not drown. We will not burn. We have the reality of baptism, and its promise of grace to bolster us. That support comes at the moment of death, but also when we are in mourning at great loss.
It’s my thought that funeral readings are chosen for one of three reasons. They might suggest something of the deceased. They might tell us something of God or of Christ. They might also be directed at the mourners.
If a person has had a long and difficult illness prior to death, perhaps this reading touches on that somewhat. I think Isaiah 43, when used at funerals, is mainly about those left behind. How do we deal with loss? How do we cope? Partly, through the agency of God: the grace that gives us confidence to continue through trials and know in our hearts that God will be with us.