Time continues into infinty and all things do happen, in essence, all things happen and don't happen with each new passing second.
Essentially, because of infinity all things that can ever happen must happen, and at the same time all things that can ever happen haven't happened aswell, as there are another infinty worth of "things" to happen after you've reached any arbitrary lenght of infinity.
If we asked this same question after 8 billion trillion years, we would still say that all things that can happen will happen in the next 9000 billion trillion years, but as each second passes we move away from the old infinity, and into a new one.
All things that could ever happen in our universe (or cosmos or whatever you wish) may occur at some point, say randomly in the 80902838734 billionith trillionth year, but the second after that passes, we continue into a new infinty, where all things that could ever happen, have both happened and not happened as infinity continues. Again that is an excellent thought. It illustrates the duality of infinity, where things happen and don't happen at a given point.
My second point was simply a further illustration of infinity.
If all things that can happen will happen, as is supposed in infinity, there will be all concievable things happening; including spiders painting all the works of art ever painted, or the sea creating shapes on the beach from shells that resemble all things, or the plants in someone's garden growing to resemble Will Smith.
Basically, if it can happen, it will; so if we can concieve of a spider stepping in some ink and walking on a page in a way that replicates the works of Edgar Allen Poe, it will happen, as we have an infinte time scale.
( I hope that makes sense, if not ask!)