I've never heard of a case where memory leaks are a good thing.
In mondern operating systems they aren't nearly as bad as 5-10 years ago. Back then, OSes where much worse at policing programs and memory leaks would cause the memory to be permanently lost until the OS was rebooted.
These days, that isn't really an issue. So the most common "memory leaks" are when things are not cleaned up properly in error and exit cases from a program. When the program is about to terminate, usually it is okay to let the memory stay un-freed, because when the program is torn down by the OS all of that will be reed any way.
While the program is running, I can think of no reason that you'd want to have memory leaks.