Changing a Profile type Machine Name broke the Admin/People search
I think this is a bug in Profile2 module.
I recreated your issue on a test installation and the same results happened. 
After I inspected the database itself I found that the machine name was not changed in the table profile but correctly changed in profile_type table.
What you could try is to manually change the machine name in the profile table and see what happens then.
Also, it might be helpful to post your issue in Profile2 issue tracker, maybe they can fix this for other users.

Good luck.