Broadcast degrade, which wouldn’t mean much for already existing conqueror civilizations looking for anyone to invade, but does mean the signal isn’t entirely endless and we don’t broadcast with the strength to reach very far (what with our only needing to send them around our planet). Our historic signals may very well never make it to civilizations advanced enough to hear them just due to distance and the fact that space isn’t a perfect vacuum; signals degrade linearly as they are overwhelmed by the comparatively much more powerful background radiation. Digitally encoded signals like the ones we send now would be even harder to detect as the information would seem random.
Additionally, if we were to stop broadcasting then our broadcast would be effectively an expanding bubble with a ~130 light-year thick surface, so while it may reach a civilization and continue to reach them for 130 years, there is a chance it would reach them prior to technological advancement and it would pass by without detection. Of course in this case we assume that a new civilization would be hostile.
The party example doesn’t really work here because there is no start time to be on time or fashionably late/early to.
Fun conversation, this is the stuff I used to love reddit for 😊