Reduce Width Left Edge Increase Width Right Edge

I am working with a Tiled background and as the left edge moves past my screen edge I want to reduce it back to my screen edge, at the same time I want to increase the width of the right edge so I don't run out of background.

More details:

I am on an endless platform running to the right. This means my backgrounds moves to the left. I obviously can't make it endless so I need a way to increase the right side width as I move to continue to see my background. For performance I feel I need to delete some of the infinite background I already ran across.

I used two backgrounds before and as one passes it deletes and adds it to the right edge but I feel like that is a sloppy way to do it when you have a background tile sprite.

I'm hoping it is something easy but called something I haven't heard of. Any help is great!

It should scroll.

My character will stay still (run in place) and the background slides from right to left giving him the perception of movement.

I do this with bullet which is all no problem. But as it slides off screen I want to remove the excess from the left side and keep adding to the right side of my background

I just updated my previous comment. Have a look at the example

Thank you for the solution. It is not exactly what I am looking for but I believe it will be an update to my old model I used so it's a great back up.

I tried to illustrate what I am looking for to see if it helps :-P

As far as I know you can't adjust the left and right bboxes independently. To achieve what you want you would have to move the object to the right which would defeat the purpose of the left scrolling background.