We know from the start of "Alone" that our speaker is struggling to find her spirituality, to feel connected to something greater than herself. She is lying in her bed thinking about how to find her soul a home. As a result of her need and quest for spirituality, she has a revelation about all people. She realizes that in order for people to find homes for their souls, they have to stick together. Community helps spirituality flourish.
There's no actual cure (in this world) for the alone-ness that the speaker describes in this poem.
The cure for the alone-ness the speaker describes can be found by re-connecting with people around us.