The ending to A Streetcar Named Desire is all about cruel and tragic irony. Blanche is shipped off to a mental institution because she can’t deal with reality and retreats into illusion—yet Stella is doing the very same thing by ignoring her sister’s story about Stanley. (See Stella’s “Character Analysis” for lots more.)
Blanche, who always insisted that she “[doesn’t] tell the truth, [but rather] what ought to be truth,” has actually come clean about reality for the first time (by revealing that Stanley raped her). But no one believes her.
Blanche’s final and very famous line, “I’ve always depended on the kindness of strangers,” is yet another example of tragic irony; what she considers “kindness” is only desire—the attention she gets from “strangers” is generally sexual in nature. (Again, lots more to say on this in her “Character Analysis.") It’s a fitting ending for a work that explores cruelty and tragedy to such a gut-wrenching degree.