Has anyone studied why homeless people refuse help? It's usually because the "help" isn't help. E.g. "you can sleep here but only if you haven't used drugs in the last week, so we'll test your blood before we let you in"
That is help. A drug addicted homeless person has two serious problems, and it's not generally viable to try to solve the homelessness problem without solving the drug addiction. Even if you were to straight up give each drug addict his own house, a lot of them will wind up selling the house to buy more drugs because it's that hard to resist the temptation when you're addicted. So, in order to help with the homelessness, you generally have to help with the drug addiction at the same time.
So an enterprising drug-dealer can buy the house for a little baggie, hire the junkie to shovel the sidewalk, and rent it out, now everyone is employed, housed, and the free market actually absorbed the cost. The dealer will pay property taxes, to keep eyes off of the other business, the junkie will be safe and motivated to contribute, what else? Oh, social services jobs don't get to practice measured goodness to Skinner Box Volunteers, and it might hurt the cause to see photographs of the yard.
So don't let them sell the house. I recommend that for all homelessness solutions. You won't capitalism yourself out of a problem you capitalismed into.
How are you supposed to help a person like that thought?
I understand that you cannot reason too well with an addict, so it might be surprising to some that somebody would refuse shelter if it meant being clean.
Still, what should be the approach then? Unconditional help?
I think it's a tough problem to solve: how far should we help drug addict in their addiction? Is the goal to help them survive, help them stop using drugs, help them find a job?