Everyone deserves shelter. Most homeless, like most housed, are not a threat to anyone. The only thing homeless people have in common is that they're too poor to get into an apartment. 

Addiction is generally a response to unhappiness, not a "choice". Being homeless is very stressful and is pretty much guaranteed to make one very unhappy. People who knew this woman said she was getting better when she stayed at Whoville, was drinking less. And then the city closed down Whoville, without creating shelter for the people who were living there. There is not enough shelter here, especially this time of year. What there is tends to exclude drinkers, like the Mission. As for where your sympathies end, that's for you to say. Here is a link to a local video about two homeless women, the second being Carrie, that might help:

It's so cold out here! 
https://www.youtube.com/watch?list=UU18T3g3ibw5lMZgqFHoXc5Q&v=QH8FdvMckM8