I think one has to be led by the Holy Spirit to take a (stranger) homeless person in. Here in Los Angeles many of our homeless are on drugs or mentally ill. It would be unwise, possibly unsafe to invite someone in that is on drugs or mentally ill.
Also once you invite them in, they can legally refuse to leave.
The Lord wants us to help others but
He also says we should be wise as a serpent.
We can always contact a Christian organization working with the homeless about the person.
This is the Dream Center ministry in Los Angeles, seven minute video worth watching.
Now that is a different story if it is your parents or your family members. Certainly you should try to help them.
I took care of my bedbound 94 year old mother until she died, little over two years ago. It meant changing diapers round the clock and more, but I knew my mom wanted to die at home.