"The matter of caring for our aged brethren and sisters who have no homes is constantly being urged. What can be done for them? The light which the Lord has given me has been repeated: It is not best to establish institutions for the care of the aged, that they may be in a company together. Nor should they be sent away from home to receive care. Let the members of every family minister to their own relatives. When this is not possible, the work belongs to the church, and it should be accepted both as a duty and as a privilege. All who have Christ's spirit will regard the feeble and aged with special respect and tenderness. 6T 272.1"
"But if any widow have children or nephews, let them learn first to shew piety at home, and to requite their parents: for that is good and acceptable before God."
Both passages emphasize the responsibility of family members to care for their own relatives, particularly the elderly. While 1 Timothy 5:4 specifically mentions widows and children/nephews, the underlying principle of familial responsibility is the same as EGW's statement about families ministering to their own relatives.
"places upon the members of every church a personal responsibility to care for them. We are not to lay our responsibility upon others. Toward those within our own borders we are to manifest the same love and sympathy that Christ would manifest were He in our place. Thus we are to be disciplined, that we may be prepared to work in Christ's lines. 6T 272.2"
"Bear ye one another’s burdens, and so fulfil the law of Christ."
Both passages emphasize the importance of caring for others within the church community. Galatians 6:2 speaks of bearing one another's burdens, while EGW speaks of a personal responsibility to care for those within the church. The core principle of mutual support and care is present in both.
"The minister should educate the various families and strengthen the church to care for its own sick and poor. He should set at work the God-given faculties of the people, and if one church is overtaxed in this line, other churches should come to its assistance. Let the church members exercise tact and ingenuity in caring for these, the Lord's people. Let them deny themselves luxuries and needless ornaments, that they may make the suffering needy ones comfortable. In doing this they practice the instruction given in the fifty-eighth chapter of Isaiah, and the blessing there pronounced will be theirs. 6T 272.3"
"Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?"
EGW explicitly mentions Isaiah 58 and connects the actions described in that chapter (feeding the hungry, housing the poor, clothing the naked) with the church's responsibility to care for its sick and poor. This is a direct and intentional connection.