Is it permissible to form a pure-intentioned friendship with a sick woman, limiting conversations with her to what is necessary?

Friendship between a man and a non-mahram woman, in its commonly understood sense today, is not permissible. However, if what is meant is speaking out of necessity or visiting, while adhering to Islamic etiquette such as lowering the gaze, and avoiding seclusion (khalwa) or touching, then there is no objection to it, as long as there is no fear of temptation (fitna). Evidence for this includes Aisha’s visit to her father and Bilal during their illness, and Abu Bakr and Umar’s visit to Umm Ayman.