This looks like a problem in asyncio. When the client closes the writer, the TLS and TCP connections are shut down. The server's writer still accept data although it is not written to the underlying ssl object:

(Pdb) writer.transport._ssl_protocol._extra['ssl_object'].pending()
0
(Pdb) writer.transport._ssl_protocol._in_shutdown
True
(Pdb) len(writer.transport._ssl_protocol._write_backlog)
2