There is/was an extension that did that at some point, but it was never used (on Linux) due to poor implementation and a desire to target low RAM machines. Mac's backing store implementation was quite heavily optimised - macOS can do on the fly memory compression and the window server uses shared memory to obtain the window bitmaps.
My memory are quite fuzzy but I think that this is incorrect here, what you're describing was only the default behaviour: you could program your application to tell the X Window server to use a 'backing store' for your window and it would memorize your window to re-render it by himself.