Personally I would say it would be wrong to take advantage of anyone "down on their luck." Yet, the line between choice and exploitation imo largely depends on whether there is support (examples of support systems are given in paragraph 2 and 3) for the person in question and this often depends on whether the person is valuable or not to anyone in particular or to society as a whole. Support can often hinder if not stop exploitation. Those without support are most vulnerable and are likely / most prone to be exploited.
I would say that the people in all three scenarios given by you, although disadvantaged, are not necessarily very vulnerable due to theoretical support systems that are in place to help them. A regular worker addicted to drugs has chosen to take drugs and is prone to be exploited but at least has the wherewithal to keep a job and to function in society and has the support system of the job and possibly his family and the community at large to offer help and advice. A single mother taking care of a sick child is prone to be exploited but if she is of sound mind and chooses to function as society legally requires, she can access, the support systems of friends, family, fundraisers to help in her situation and is not necessarily at a disadvantage. Nor does she have to turn to "immoral" activities, including the example given by the OP, to sustain the health of her child. A minimum wage worker (has chosen to work in that capacity or more likely chosen to be at that economic level but) is certainly prone to be exploited. Yet the minimum wage worker is at least guaranteed by the government a support system of fair treatment and "adequate" pay.
If any of the aforementioned people cease to function mentally in a "normal" (as society dictates) capacity there are support systems available to them in terms of institutions, clinics, hospitals, the legal system, etc. that offer some guidance and support for them. Friends and family can often guide those who need treatment to the appropriate locale. These support systems are also available to the homeless but this implies that the homeless are aware of and can locate, access and potentially pay for the support.
The homeless woman in the OP made a poor choice but those who are desperate and who moreover lack any sort of support system (even and often including friends) are more prone to make poor choices and are in my opinion more prone to be exploited. There are few support systems / protections in place that will be accessed by them and even they can work against the homeless. In my view, as a homeless person she should be treated with a level of dignity even though she is not necessarily dignified in her appearance, social standing or in her choices. Why, because she has basic human rights that should be honored, particularly the right to not be degraded, even where / when there is a request / choice made for degradation. These basic rights also apply toward treating prisoners or illegal refugees with decency. This is also the same argument for treating the drug taking employee, the single mother with a sick child and the minimum wage worker with decency. The decency argument applies toward those with support and to those without any support.
This can develop into a long argument but at a basic level I don't see how people can endorse overtly unfair treatment of people who are in need and then get mad at workplace racism and gentrification in the same breath. After all they chose to apply to work for that company for money and they chose to leave their neighborhoods for money and the racist and the gentrify-er are only using leverage.
Be guilty of doing the very thing that you despise brehs. I think they have a word for that ... hypocrisy.