The tactic for removing dried cat urine smell from a rug is different from cleaning wet cat urine. When fresh, cat urine is acidic, with little odor. When dried, cat urine turns to alkaline salts, creating an environment for stinky bacteria to grow. If your rug is washable, it is possible to remove the pungent urine smell with basic distilled white vinegar.
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Fill your washing machine with water and one cup of white distilled vinegar.
Put the rug in the washing machine and run through a complete wash cycle.
Refill the washing machine with water and add laundry detergent, using the amount recommended by the manufacturer. Run the rug through a complete wash cycle.
Remove the rug from the washing machine and hang dry. Fluff the almost-dry rug in the dryer.