Aunt Larisa is Sasha's dad's sister, and she lives with her husband (who isn't named) and her new baby (who is also not named). When Sasha's dad is arrested, he turns to good old Aunt Larisa, just like his dad tells him to.
So why won't Aunt Larisa take him in? It seems like a no-brainer, especially since Sasha now has nowhere else to go. Turns out, she and her husband are afraid that they would be in line for being thrown in the clink if they allow him to move in: "We just had a baby. We have to stay alive" (9.16). Oh yeah? What's Sasha—chopped liver?
Aunt Larisa does show kindness to her nephew, though: "I knew she'd come, and she does, arms reaching out and pulling me in" (9.14). He receives physical comfort from her (which is in short supply), and also money for the streetcar, which allows Sasha to get to school the next day. It's small potatoes, sure, but it's better than no potatoes at all.