What does " I have always depended on the kindness of strangers" mean?

I always thought it meant that Blanche DuBois was a rather neurotic, insecure and needy woman who constantly sought someone (a man) to generally take charge of her life and her emotions and who would shield her from her problems, rather than make any effort to cope with them herself and take responsibility for her self and her life

Her attitude was that 'someone' would always happen along to assist and protect her. In short, the next man was always the one who would finally 'rescue' her from her drab life.

Sorry I can't offer more, but I haven't opened 'A Streetcar Named Desire' or seen the film since the early 60s and have no copy.

Have you Googled Tennessee Williams?