How might you help someone with severe depression to live alone?

Gently: Let them know that they are not alone even if they are the only one in the home. Offer friendship & support. If someone has disabling depression, they may occassionally need a little help in order to continue living independently. Although you aren't taking on the role of caretaker- let the person know you are a telephone call away.

Be a friend & model: In addition to letting them know you care and being available, sometimes it helps (& can preserve your energy & sanity) to be a bit of a teacher & model for the depressed person you care about. Invite them along when you do something to treat yourself (doesn't have to cost, maybe a hike in a beautiful park), and help them see, step-by-step, how you take care of yourself & your own happiness.