How to move a video over a mask in Final Cut Pro

I'm not sure I understand your purpose for doing so, but what you can do to create a "stationary" mask is apply it to what people normally refer to as an "Adjustment Layer". I'm sure you can find one (free) easily. If you have Motion, simply create a new Title template, delete the default text and save as Adjustment Layer (more accurately, it's a Clone Layer - which a photoshop user would understand better.) It will automatically be published to Final Cut (pay attention to the Category option when saving so you can place it and find it in a logical place.)

Clone Layers affect *everything* below them, so if you have media clips and other titles or generators underneath the Clone's level, they will all be accumulated into the Clone.

HTH

You don't have to purchase Motion!

You can download "Clone Layer" here:

https://fcpxtemplates.com/?smd_process_download=1&download_id=24013

You need to go into your Home folder. You'll find a Movies folder.

You will need to go into Movies and create a folder called (exactly) Motion Templates.localized.

When you type Return after naming Motion Templates, the ".localized" part will likely disappear -- that's normal.

Open the Motion Templates folder and create a new folder called Titles.localized.

Open Titles, and create another new folder. This will be the Category name of the content inside. You can name it anything you like — try Editing Assistants.

Inside the category folder, place the Entire Clone Layer folder inside.

It should be available in Final Cut Titles Browser as soon as you finish installing it. (If you run into trouble, let me know.)