Un-de-duplicating strings

MATL, 7 bytes

Y'to+Y"

Try it online! Or verify all test cases.

Let's take 'ABBA' as example input.

Y'   % Implicit input. Run-length decoding
     % STACK: 'ABA', [1 2 1]
t    % Duplicate top of the stack
     % STACK: 'ABA', [1 2 1], [1 2 1]
o    % Modulo 2
     % STACK: 'ABA', [1 2 1], [1 0 1]
+    % Add, element-wise
     % STACK: 'ABA', [2 2 2]
Y"   % Run-length encoding. Implicit display
     % STACK: 'AABBAA'

Retina, 11 bytes

(.)\1?
$1$1

Try it online - contains all test cases

Perl, 16 bytes

15 bytes of code + -p flag.

s/(.)\1?/$1$1/g

To run it:

perl -pe 's/(.)\1?/$1$1/g' <<< 'HEY'