Does this have to be done in bash?
I would first suggest using set -xv to see if all your variables are being populated the way you think they are.
read -r a x y z <<< "$a"
Assuming the correct data is stored in variable 'a', x will be first word, y will be second and z will be the rest of the line.
Based on your desired output that would mean from the input file:
x = another
y = string
z = to examine
So not sure I see how you would ever get the correct output??