The simple answer is that they are, like us, supposed to be giving thanks, too. But for what?
Well, this is my considered answer. Everybody, whether in plenty or in want, is supposed to be giving thanks for the same thing. It has much less to with the people around the table and their prosperity or good fortune than with the understanding of their thanksgiving in the first place.
Habbakuk got it:
Although the fig tree shall not blossom, neither shall fruit be in the vines; the labor of the olive shall fail, and the fields shall yield no meat; the flock shall be cut off from the fold, and there should be no herd in the stalls: yet I will rejoice in the Lord, I will joy in the God of my salvation.--Habakkuk 3:16-17
There is only one thanksgiving to which we are called--thanksgiving to God for Himself.
Any unbeliever can be thankful to their own deity--karma, fate, circumstance, personal fortitude--for the plenty of their life. It's easy. It is only the person of faith that can give thanks in want.
Think about it.
Sooner or later, everybody has trouble. Without the inspiration of the Holy Spirit, trouble brings misery with it, but with the Spirit, trouble brings focus. While not devoid of sadness and difficulty, Spirit-led troubles include a sense of purpose and direction. They take us someplace. Our circumstances, whatever they are, are a gift from God. Do we give thanks, then, for illness or hunger, or loneliness or poverty? Yes, for these, too. God, after all, either brings them or allows them. Whatever our condition, it came to us through God.
Rejoice in the Lord always.--Philippians 4:4
Troubles are God's assurance that we are ready for more of Him. If I am ill, God changes me to find His healing, even when He doesn't bring a cure. If I am lonely, He calls me to His side. If I am afraid, He calls me to trust.
So it's Thanksgiving and what are we to be thankful for? Give thanks to God for God.
Thanksgiving is not about plenty, even when we have it. Thanksgiving is about the places in our lives where we are starving for God's riches. It is where God opens His arms to us as only He can. It is about how we find God more in what we still need than in what we already have, about resting in Him when everything else has fallen short.
It is a sweet, poignant "Thank you" sung in the dark.