After her graduation from the Petrograd Conservatory, Yudina was invited to teach there, which she did until 1930, when she was thrown out of the institution because of her religious convictions and vocal criticism of the Soviet leadership. After being unemployed and homeless for a couple of years, Yudina was invited to teach the graduate piano course at the Tbilisi State Conservatory in 1932–33. In 1936, on Heinrich Neuhaus's suggestion, Yudina joined the piano faculty of the Moscow Conservatory, where she taught until 1951. From 1944 to 1960 Yudina taught chamber ensemble and vocal class at the Gnessin Institute. In 1960 Yudina was thrown out of the Gnessin Institute because of her religious attitudes and advocacy of modern Western music. She continued to perform in public, but her recitals were forbidden to be recorded. After an incident during one of her recitals in Leningrad, when she read Boris Pasternak's poetry from the stage as an encore, Yudina was banned from performing for five years. In 1966, when the ban was lifted, she gave a cycle of lectures on Romanticism at the Moscow Conservatory. According to an otherwise unsubstantiated story in Solomon Volkov's book Testimony, which claims to represent the memoirs of Dmitri Shostakovich, one night in 1944 Stalin heard a performance of Mozart's Piano Concerto No. 23 on the radio performed by Yudina, and asked for a copy. It was a live broadcast so officials woke up Yudina, drove her to a recording studio where a small orchestra had quickly been assembled, and made her record the concerto in the middle of the night; a single copy was pressed from the matrix and given to Stalin. In another apocryphal story, she was awarded the Stalin Prize and donated its monetary portion to the Russian Orthodox Church for prayers for Stalin's sins. But the existing recording of the Mozart concerto with Alexander Gauk dates from 1948, so the date 1943/1944 could be wrong. Yudina remained an uncompromising critic of the Soviet regime. She died in Moscow in 1970. Yudina's playing was marked by great virtuosity, spirituality, strength and intellectual rigor, with a highly idiosyncratic style and tone. Sviatoslav Richter said of her playing:
She was immensely talented and a keen advocate of the music of her own time: she played Stravinsky, whom she adored, Hindemith, Krenek and Bartók at a time when these composers were not only unknown in the Soviet Union but effectively banned. And when she played Romantic music, it was impressive—except that she didn't play what was written. Liszt's Weinen und Klagen was phenomenal, but Schubert's B-flat major Sonata, while arresting as an interpretation, was the exact opposite of what it should have been, and I remember a performance of the Second Chopin Nocturne that was so heroic that it no longer sounded like a piano but a trumpet. It was no longer Schubert or Chopin, but Yudina.
Yudina was portrayed as a character in Aleksei Losev's novel Woman as Thinker. The flawed heroine Losev created was a woman musician who spouted philosophy but held herself to lower standards. The novel has been criticized as an outlet for Losev's difficult relationship with Yudina, and as a poor example of his capabilities as a writer. She was offended by the book, and ended their friendship in 1934. In 1989 David Zane Mairowitz wrote The Stalin Sonata, a radio drama loosely based on an encounter between Stalin and Yudina. It won a Giles Cooper Award. Yudina appears in the French graphic novelLa mort de Staline, which retells the apocryphal concerto story from Solomon Volkov's book Testimony and fictitiously portrays her writing a castigating letter to Stalin that prompts his death. In the novel's 2017 Anglo-French film adaptation The Death of Stalin, she is portrayed by Olga Kurylenko.
