Where can I find rendered Stabilization files?

It might help if you describe the workflow a little bit. For example, did you get source footage from your customer to do some work on the editing, with the idea that you would give that customer an 'exported' product ?  Like a video product ?

Is that customer now saying that they want to send the 'project' ( your premiere pro project with your work done on it ) to someone else to work on it in an NLE ?

????

Rendered files are usually stored in the cache location that you selected in your preferences. Usually on a separate drive then your project files if you use multiple drives for faster performance.

Those cached files are described by the program ( numbers and letters and who knows what else ) and are NOT new 'video files', like CLIP 1 STABILIZED.MOV

They don't make sense to ANYTHING except your specific computer and your specific timeline and those clips you stabilized.

Nobody else on earth will be able to understand what they are.

Soooo, if you describe what you want to do better, and what the customer wants to do, you may find that you want to do something like, export your project to share with someone using the same program ( collect and save to an SSD or something and mail to them )…..or you can go the XML route with source materials for a different NLE or who knows what... cause I have no clue what you are trying to do along with your customer

Warp Stabilizer analyzed files are embedded in the project file.

The rest is in the Video Preview folder usually in the same folder as your project.