There is a deliberate contrast between this verse and verse 17. In verse 17, God is referred to as being forgotten by nations, but the needy are not forgotten in this verse. In this context, both aspects of the contrast matter: those whom God "remembers" are those who follow and honor Him. Despite their wealth, the unbelievers will still be held accountable, while even the poor who believe will be redeemed.
We can be assured that our Heavenly Father will never forget those who remember him. Earlier in the psalm, David praises the Lord for His righteous judgment in the past, while the last verses contain a request for safety regarding his current situation and future. The first segment acknowledges God's wonderful acts of deliverance in the past, and the last segment requests God's continued protection and provision in the future.
As men of faith, we will always experience trials and tribulations in this fallen world. Nevertheless, the Psalmist offers hope for those who trust in the Lord, even in times of lack or feeling forgotten or afflicted. Being God's children, we are sure of His protection since we have received forgiveness of sins and eternal life in His hands.

Dear Heavenly Father, it is a blessing that Your eyes are not closed to the hardships and difficulties I am facing at the moment. Your love and trust will never let the needy be forgotten, but You have prepared something better for them. I thank You for all Your goodness and grace towards me and for protecting and delivering me from those who sought to harm me. Despite living in the world, I understand that I am not a part of it since I am saved by grace by faith in the lovely Lord Jesus.
In Jesus's name I pray. Amen.