bad litterbox behaviour

kansasherd here:
   
Our cat has been diagnosed as having kidney failure. She is 19 years old and has lost some weight also from this. We feed her science diet k/d only. Lately she has gone to missing the litter box to going on paper or plastic. We have tried to watch and put her in the litterbox when she strays elsewhere but to no avail. We even changed the litterbox, we are running out of ideas, she used to be very clean and fastidious so we are sure this is because of discomfort going #1. She seems ok with #2 most of the time but not always.

I know you didn't ask this, but... Your cat, at 19, is very, very old. You have to realize that a 19 year old cat with kidney failure is not going to live much longer. I speak from experience: I've had 2 old cats die of kidney failure; they declined quickly. When she stops eating, it's time to let go.
   
Cats experiencing kidney failure frequently piddle in the wrong places; they seem to not want to make the effort to get into the litter box.
   
Try a flat shallow tray with puppy pads in it, in place of her litter box, so that she won't have to climb into the box. The lids of the large plastic storage bins would work. Put it in the middle of a larger area with a plastic lining. First time, sprinkle a little soiled litter on it, so she smells herself on it.
   
When she's left alone, you should confine her to an area where she has the puppy pads & a place to sleep, so she won't be going without you knowing. This can be accomplished by using a large cat pen, laid on its side for maximum floor space: EXAMPLE LINK, Cat Playpen: http://www.drsfostersmith.com/product/ prod_display.cfm?c=3261+16901+663&pcatid=663
   
You could also keep her in the bathroom when you're gone - just make it comfortable for her. Or any other small room without a carpet.
   
You could also use a child's playpen or a puppy pen. LINK, Economy indoor-outdoor dog pen: http://www.drsfostersmith.com/product/ prod_display.cfm?pcatid=16677
   
I recommend a heated bed or heat pad for her, as old sick cats feel cold easily. Drs. Foster & Smith, CareALot Pets & Amazon have them for sale. Look specifically for a cat heating pad or heated bed, which heats to 101 degrees, a cat's normal temperature.