19 year old cat misses box!
Until about 6-7 months ago our cat, Chip, used her box for 18 years without any messy misses.
Now, each visit leaves a puddle outside the box.
I have stopped using a standard size cat box (suggested by the vet) and use a very large plastic storage box that she can get in/out of very easy.
She does go into the box, the urine is half inside and half down the outside of the box and on the floor. Chip makes a very feeble attempt to cover the wet inside the box.
I have tried "scooping" feces after each use, keeping the box very clean, and I have left the box "dirty" for a day or two... nothing helps.
Chip's in good health for her age.
I'm sorry to hear that your cat is having trouble. Making it as easy possible for her to get in and out is probably a good move no matter what.
This is a tough one and I'm not sure you can train her out of it, so my ideas are focused more on dealing with it than changing the behavior.
If you use a tall plastic bin that has high sides, she won't be able to "shoot over" the side. You'll need a cutout so that she has easy in/out access, and hope that she doesn't choose to back herself up to the cutout.
So that's one idea.
Another would be to make some high sides for the box you've got, but again you need to leave a low side for access, so that only works well if she never points her back end toward the low side.
If she uses the same area of the box every time, these might be an option.
To catch any spillover, you can place a "puppy pee pad" underneath the box. They go by various names such as "pee" and "wee" or training pads. Some are flimsy and disposable, others are washable and reusable.
Another idea for the spillover is to put the litter box in a tray, such as those made to go under washing machines.
One of our visitors left a comment that for his older cat, he used child's wading pool with doggy training pads
I'm guessing that since you didn't mention it that your vet didn't have any concerns or know why she's doing this suddenly. In addition, I'm assuming that you didn't change litter type on her or make any major changes right before this started.
I hope that helps. Please leave any feedback or questions in the comments and let us know how she progresses.