In the past you may have imported, say a blue circle from a SOURCE FILE in Photoshop, into a TARGET FILE in Illustrator containing, say, a red square. Then you saved the Illustrator file, and forgot about it. If imported incorrectly (and you can’t just Edit/Copy from PS and then Edit/Paste into ILL), it caused an error message when you opened the Illustrator file much later on, which brought you here to get a solution. Welcome!
What happened, technically and behind the scenes, is that a LINK was created between the PS image and ILL. The terrific idea behind linking is that whenever you change the PS image, it will automatically update every ILL file that imported that image. This is a great feature when operating under strict controls that never change. But it causes error messages and a lot of headaches when, likely, the source file in Photoshop changed significantly (like a name change) or was deleted to free up space, or any number of other situations.
This is my solution, and it involves breaking the link:
In Illustrator: I found the best process is to start by opening a new blank file, and NOT work immediately with the target file.
Click File / Place
Choose the source Photoshop file to import
Click OK, and the imported file opens in Illustrator.
Select the desired layer, and copy
Now go to your target file
Click Edit / Paste in Front
Open Links Panel
In Links Panel, open fly-away menu
Click Embed Image
Dialog box pops up
Click Convert Layers to Objects
File / Save target file
Close and reopen to double-check if the Link is broken, so no future mishaps with deleted linked files.
No more linked images, no more headaches.