How to give access to inactive user profile?
The View Profiles Permissions module will work for that purpose: https://www.drupal.org/project/view_profiles_perms.

In order for this to work, you will also need to give your blocked users a Role.

It is not the primary function of the View Profiles Permissions module, but there is more information about this specific issue here: https://www.drupal.org/node/2490934

Additionally, You can use the Rules module to automatically assign a role to users when they become blocked.

Steps:


Install and Enable the View Profiles Permissions module
Create a role called "Blocked"
Give permissions to anonymous users to "Access to Blocked profiles"
Assign the "Blocked" role to all users who are blocked (aka Inactive, Old, Disabled)
Extra Credit: Install/Enable the Rules module and a new Rule that automatically assigns the Blocked" role to users when they become blocked.