Is there a way to have an event stay in the window, (for example the bottom right visible tile) at all times?
Yes and no...
I'm assuming you use a map event for the display?
It can be done, but it requires quite a bit of thought to pull this off - that's why most people use scripting instead of eventing for HUDs.
1) Map events can't be transferred between maps - that means you need a map HUD event on every map, and you need their code started again whenever you enter a new map.
2) Common events (which are independent of the maps) don't have a display, you can only use them to display pictures on all maps. However, you can place some coding into them and call them from map events - that way you don't have to enter everything anew for the map events.
3) If you make the map event "above player" and "through" it will move everywhere on the map - and then you can use a check on parallel to set it to a location relative to the player on the screen.
However, making this parallel check a common event (theoretically better) will require you to make sure that the HUD-Event has the same ID on all maps - for example it's the first event placed on all maps to get an ID=1 everywhere.
As you can see, creating a HUD with events is not easy - you'll better off using or writing a script for it.
If you tell us what it is supposed to do, we might be able to point you in the correct direction.