How does the value of system variable max_allowed_packet affect the result of a string-valued function?

String-valued functions return NULL if the length of the result would be greater than the value of the max_allowed_packet system variable. Actually, max_allowed_packet is a dynamic global variable which can accept the integer type values. These values can be set for a session only. It can accept 1024 as the minimum value and 1073741824 as the maximum value. The by the default value of this system variable is 1048576.