It is not normal for a spayed, indoor kitty to suddenly begin such behavior.
Whenever a formerly clean kitty begins to soil out of box, she is usually trying to communicate some sort of pain or distress to her human "mom" or "Dad"
Cats may not seem unwell because it is their nature to hide an illness as long as possible but if the urine or stool is abnormal in any way - that will be your first clue. If her appetite is different that is an indication as well.
Your cat may have a urinary tract infection even though she is leaving stool. Cats "talk" with their waste.
UTI's must be treated with an effective broad spectrum antibiotic like Clavamox or clidamycin and for a long enough duration so all bacteria is eradicated. If not, they will refluorish, stronger and more resistant and re infect her . In addition, the bacteria can become tolerant of the same antibiotic so the medication should be varied for best results.
Anything new is very stressful to a cat because kitty's HATE change and stress can lead to illness so you want to watch for any developing symptoms.
Give her a teaspoon of plain yogurt every day. That will keep "good" bacteria in his colon.
She can also have one drop of unsweetened cranberry juice every day to lower the PH of herstool and urine.
If this continues or gets worse she should be checked.She is not just doing this to annoy you or because he got mad as cats do not think like that - she may not feel well and is trying to let you know about it.Or she is confused..
Sometimes cats become "picky" about the condition of their box and do not want to share or use the same one for both things..Try adding an additional one and see if that helps.
Also try cat attract litter sold in pet supply stores. Clean any soiled areas with an enzyme product so he can no longer smell it. Bleach will not fool a cats nose either
She may be marking in a desperate attempt to reattain her head cat status or she may just be intimidated or sick.
Spray with feliway http://www.catfaeries.com/ to fool her into thinking items are already marked. Try rescue remedy sold in pet supplies and is rubbed on the gums.
Clean with an enzyme product like zero odor or odor mute because regular detergents will not fool her either. With carpet you must lift it and treat the padding.
Please let me know how she is doing. if you still have questions, I will always be here for you.
I hope she stops real soon and feels better!