Matthew 25:40 contains one of the most direct statements Jesus ever made about the theological weight of care: "Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me." The person being cared for — who cannot say thank you, who may no longer know the caregiver's name, who has become fully dependent — is, according to Jesus, the face of the king. The care given to the diminished person is given to Christ.
Isaiah 46:4 is directly applicable to the person with dementia: God carries to old age, to hoar hairs, to the end. The person whose memory is failing is not less known by God for their forgetting. God's memory does not decline with theirs. Deuteronomy 33:27 describes God's arms as everlasting — underneath the person whose body and mind are failing, the eternal arms are still there.
Commentary is from a charismatic Protestant perspective, drawing on KJV text and public-domain sources including Spurgeon, Andrew Murray, and Matthew Henry.