It is possible to stop a script execution and resume it later. To do so, the application must take care of storing the execution ID in a custom table and associate it with some user ID. See Cleaning Up Application Data for more details.
Provided the IEGEXECUTIONSTATE table hasn't been cleaned up and the script definition hasn't been modified, a script execution will be resumed by passing the executionID parameter to the IEG Player in the same way it is done when starting a new script execution.