Delete/ Deactivate account in a separate block
What you are describing will require a custom module that will provide the non standard functionality.

You will need to provide hooks for blocks (hook_block_info and hook_block_view) producing forms using the FAPI to produce the forms as you are showing in your mock. 

Deleting an account would require using form validation to test that the username and password is correct and matches the content that you are viewing as well matches the user that is logged in. Once validated you would call the user_delete function, however be aware that this will delete all content owned by the user. 

Disabling or Deactivating account will require a hook_block_info and hook_block_view  as well the form using the FAPI as well a subset of the  validation mentioned above, then calling the user_cancel function passing in the appropriate arguments. 

The forms could be rendered using...
1. the blocks ui with conditional visibility settings.
2. at the theme level using a preprocess_page hook in template.php
3. other...

As Drupal is like a swiss army knife and this is one of many ways to solve the issue.