Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Zoe is not passing stools normally, and now may be constipated.
Because Zoe is a tail-less cat I wonder if her intestinal motility is slower than normal due to poor nerve function. Tail-less cats are known for having abnormal nerve function at the end of their spinal cord (where the nerves that control the colon come off of the spinal cord) as the genetics that lead to short or absent tails can also affect spinal cord development. If spinal arthritis develops then nerve function is further compromised. If she's ever had any stiffness or difficulty with jumping or climbing stairs then I suspect that she does have some neurologic based trouble. But even if she is able to move normally she may still have altered colonic motility.
If it's been several days since she passed a stool and if she starts vomiting she is likely beyond home help.
At that point she will need a veterinary visit and probably an enema to get her right.
Long term we can't change her conformation but we can help with inflammation and arthritis symptoms with a glucosamine/chondroitin supplement (like Cosequin) and an omega 3 fatty acid supplement like 3 V Caps or Derm Caps. In some cases using a nonsteroidal anti-inflammatory or pain medication like Gabapentin for very short bursts of time may help as well.
For now if she is still eating you can also try adding tuna juice or sardine juice or low salt chicken broth to her food to get more fluids in. Ideally from this point on she would eat a canned senior food that is higher in fiber. The fiber helps improve gastrointestinal motility and canned food is simply higher in fluids.
Another option is adding a tablespoon of canned pumpkin (not pie filling, just pumpkin) to her current canned food once or twice daily. Some cats like the taste and will eat it directly or sometimes mixing it with canned kitten food gets them to eat it. The combination of increased moisture and fiber is very helpful for many cats.
Another option to soften stools is Miralax, 1/8ht to 1/4 of a teaspoon once or twice daily to soften stools to start. You can mix this with some canned food or baby food. Start with a low dose and increase it if you must.
Make sure to add fluids to her meals, either warm water or low salt broth.
If she has any sort of early organ disease, primarily kidney failure, that can cause drier, more difficult to pass stools. An examination, bloodwork and urinalysis will help diagnose this.
If adding fluids and canned pumpkin or Miralax aren't enough long term then she may need medication from her veterinarian.
Because she isn't eating well and has vomited I recommend that she be seen promptly as that may indicate obstipation, which is severe constipation with very large, impossible to pass stools that must be broken down manually under sedation.
We may also need to use a medication called lactulose chronically to keep stools soft and easy to pass, and sometimes we may need to add a medication to stimulate colonic motility, for example Cisapride.
There are two options for feeding a cat with chronic constipation. One is to increase fiber as a stimulant to get the colon moving. I mentioned increasing fiber in his diet earlier in my write up, and that's what we usually start with. The other option is feeding a highly digestible diet so very little stool is produced and there is less to move through the colon. Sometimes it takes trial and error to see which one will work for your kitty. Whichever one you use make sure to feed canned food, add water or low salt chicken broth to improve his hydration and offer plenty of water to drink. Perhaps a kitty water fountain will encourage her to drink more.
Hills i/d is a low residue diet designed to produce little stool. Hills r/d or w/d are both high fiber foods to stimulate colonic motility. If she responds well to fiber but doesn't like those foods you can use 1/8th of a teaspoon of Miralax added to her food as well to keep stools soft.
Some cats with chronic constipation can get a condition called megacolon, where the colon loses its propulsive, muscular function and stools sit in it becoming large, dry and difficult to pass. In those cases we try diet manipulation (usually low residue diets work best), and we must use drugs like cisapride to improve motility as well as lactulose to soften stools. If the colon simply isn't working though these cats will need surgery to remove the diseased portion of the colon. They usually do quite well after surgery.
Best of luck with Zoe, please let me know if you have any further questions.