Comment 6 for bug 1822736

It is yet unclear what the root cause of this issue is - libpam, crypt, passwd and sudo seem like primary suspects. The 256 character password is hashed to a value which still allows a TTY login to succeed. Also, passwd run by a different user in the context of the affected user (using sudo) still works. So apparently it only breaks for the logged-in user. This may help identify the root cause.

pam_unix(8) (on bionic) states:
  The maximum length of a password supported by the pam_unix module via the
  helper binary is PAM_MAX_RESP_SIZE - currently 512 bytes. The rest of the
  password provided by the conversation function to the module will be
  ignored.

Regarding passwd, I was told this on IRC:
  passwd uses getpass() to read the password from the user, and testing just
  getpass() alone shows it will return up to 4095 bytes long (i.e. truncates
  at that length).