Sorry I have to disagree...I believe it would work perfectly.

If the OP created a job that ran the package I'm describing say every 5 seconds, the package does a check for a file(s) present in the folder. If no files exist when the job runs the loop container does nothing and the job completes successfully. In the event there is a file present, the execute SQL task inside the container fires off the code to execute the SQL Agent job they want to fire based upon the existence of a file.

I have an identical process in place (but checking only every 5 mins). Obviously there's more elegant solutions available but this will work for the issue they're describing.