At first I was thinking this is impossible. Aside from a disgusting answer I still think it's impossible but I'll give it a go.
I imagine this is what happens in this week episode of Yankee takes the Browns to the Super Bowl Season 1 Episode 1 :

Having been trained at an early age to always check quality and quantity of toilet paper ( ruined a "fancy hand towel" as child, you can figure out the rest) I see there's only one square left. Being a good judge of what's about to come out of me I'm worried. It's not that runny diarrhea shit as that would be easier to just "dab it" clean. It's going to be a chunky corn and peanut encrusted turd.

The grunting, pushing and praying begins. Flasploosh....a nice heavy log breaks the darkness that is my rectum and plops into the bowl causing a definite splash back. Some softer smushier turds follow suit. Once the damage is done and over with and now having a properly soaked scrotum I ponder what I am to do. The unthinkable must be done.

I reach down bare handed and wipe my ass. Recalling the times as a child of playing with toy bulldozers. Brrrrr....zooooo errrrrr.... sound effects for dramatic effect. I scoop and fling the excess poop with each wipe. Once done I wipe the poop from my hand with the single sheet. I think it's better to clean a little shit off your hand than a lot of shit off your ass with a single sheet. However, having used the last sheet I realize my down fall. There's another source. The now unexposed cardboard toilet paper roll. I should have just used that.

Realizing the error of my ways I promptly leave the West Wing guest bathroom and shake POTUS'S hand.