First, check if the files are transferred to your MacBook Air successfully. If you can't find them on your Mac, it means the files haven't been moved successfully from your USB flash drive. The reason why your USB flash drive is empty now is that the USB drive gets corrupted due to unsafe ejection.
To repair a corrupted USB drive on Mac, you can use Disk Utility.
- Open Disk Utility from Finder > Applications > Utilities.
- Connect the USB to your Mac, and click View > Show All Devices in Disk Utility.
- Select the USB drive from the left device list and click First Aid.
If the Disk Utility failed to fix the corrupted flash drive, then your USB drive may get damaged severely, you'd better replace it or reformat it to use. However, reformat will wipe all data on it. Since these files are very important to you, you can use professional data recovery software to retrieve them first before reformatting it.
There are many data recovery apps in the market, iBoysoft Data Recovery for Mac is one of the best USB data recovery software that can help you recover lost data. iBoysoft Data Recovery for Mac app works on macOS 13/12/11/10.15/10.14/10.13/10.12 and OS X 10.11 smoothly and is able to recover disappeared/missing/deleted files from corrupted USB drives, external hard drives, SSD, SD card on Mac. This app also has a simple UI and is easy to use.
Now, do the following to get files back from your corrupted flash drive on your Mac.
First, free download iBoysoft Data Recovery for Mac and launch this USB drive recovery app.
Next, click on Storage Device from the sidebar. From the storage device list, choose your flash drive.
Finally, click Search for Lost Data to scan all lost files on it. If you're lucky enough, the lost files will be listed in this app, you can select all the files you need and click the 'Recover' button to recover data and store them on your MacBook or another healthy external drive to avoid data overwriting.
If your data is safe now, you can format the USB drive on Mac to use it again. Remember that do not physically eject your USB drive from your Mac next time. Instead, safely eject it to avoid data loss and a corrupted file system.