Yes, you can recover the data. But you need to take your Mac hard drive (I do believe you are using Mac, if not, you will not ask question here) to the repair shop to fix.
When the hard drive is fixed, you will find that you got a "new" hard drive-all the files are not in the hard drive anymore. But this doesn't mean you can not recover files. I always consider that fix the hard drive like formatting the hard drive. The operating system will not really delete the files. It just delete the catalog and free up the space of the files so that there is enough space for you to store the new files. But if you put new files into this drive,the new files will occupy the the space which is belonging to the "deleted files", this is the so called data overwritten situation. Once this happens, you will lose the chance to get back your files.
Maybe you can try uFlysoft Data Recovery for Mac, it can recover empty trash on Mac only in three steps:
Step 1. Launch the software to scan the device where your files deleted
Step 2: Preview the scan result files and make mark if it is the one you find
Step 3: Recover files