Make `envsubst` fail if a variable is not defined

I have a file with a large number of variables in it.

$ cat message.txt
Hello, ${LOCATION}! You too, ${PERSON} ;)

If PERSON is not defined, envsubst replaces it with nothing:

$ LOCATION=World envsubst < message.txt
Hello, World! You too,  ;)

How can I make envsubst fail with a non-zero exit code (or something reliable) if any of the many environment variables in the file isn't defined?