The dog is missing. He shouldn't have let the dog go out of the house alone. The possible meaning of the sentence is:
A.
He is being praised for having let the dog go out of the house alone.
B.
He is being asked to let the dog go out of the house alone.
C.
He is being blamed for having let the dog go out of the house alone.
D.
He is being expected to find the dog that has gone out of the house alone.