Toward the end of the play A Streetcar Named Desire, Blanche meets her tragic end. She is sexually violated by her sister's husband, Stanley. This was the culmination of a cycle of bullying, threats and harassment caused, in part, by Stanley's perverse want to control Blanche the way he controls his own wife.
Stanley also wishes to expose Blanche's past in order to diminish her and make her socially disappear for his own sick purposes. When he finally rapes her, she becomes a completely broken woman who loses her mind.
The line "Whoever you are, I have always depended on the kindness of strangers" is known as Blanche's "famous last words." She says those words to the doctor as he leads her away to the mental institution.
Essentially, what the words mean is that Blanche, once rich, popular and independent, has ended up in an abyss of disrepute, poverty, and debauchery. She switched her life's moral code, wasting way in meaningless sexual encounters for the sake of basic but temporary comforts: company, monetary benefit, attention, a need to feel wanted, and temporary satisfaction.
All of these ephemeral things depend entirely on "kindness"—sexual attention or physical attraction—from others. These two variables, however, are just like the things that Blanche gets from them: shallow and temporary.
Therefore, what Blanche is suggesting is that she is no longer in control of her own actions, nor of her life. Granted, she had lost control way before she actually lost her sanity. Still, then and now, she depends on that "kindness," "whoever" it comes from, whether it is the doctor leading her out the door, or Mitch, or any of the guys from her past.
These words are also powerful in that they completely disempower and disenfranchise Blanche. The irony is that, at all times during the play, Blanche attempts to present a facade of someone who is "put together" and in control of what she wants; someone who is even presumably planning for her future. To openly state that she depends on kindness renders her nothing short of a beggar, something that the true Blanche Dubois would have never allowed herself to be.