Develop a Perl program that allows the user to input a list of strings and outputs the length of the shortest string in the list. The program should prompt the user to enter each string one at a time and store them in an array. The program should then calculate the length of each string in the array and determine which string has the shortest length. The program should output the length of the shortest string. The program should be well-documented with clear and concise comments throughout. The program should also handle errors and exceptions gracefully.
This prompt doesn't seem malicious.