Use your operating system's search feature to search all hard disks for (one of) these photos.
If Lightroom can't read JPG or TIF files, most likely the files are corrupted and unusable. I would try restoring the photos from their backups.
I have done that. The files must be somewhere on that hard drive, its the only one being used by LR. I have even tried looking in folders (manually) for a few of the problem files that I know came from its folder. Its nowhere to be found.
If there is someway in LR to ignore those files when syncing, that would work too.
Instead of synchronizing a folder, you could Import only the photos you specifically want.
I have done that and that works, but using the synchronizing folder updates any files changed, moved to other folders, or deleted. This is how I have always done it for years.
Syncing folders in LR does not update changed files. Once a file is in the LR catalog it is in the LR catalog. If you are using Adobe Camera RAW to do any edits then an up facing Arrow with 3 lines to the left of the arrow will show and clicking that will allow you to either "Import Settings from Disk", reading the edits made in ACR, or "Overwrite Setting" which will replace whatever edits done in ACR with whatever LR has recorded in the catalog file.
Sure doing a Sync Folder will auto import those changes made in ACR but I must ask why are you making changes in ACR when LR has the exact same system for editing RAW images (ACR is Built Into LR. That is what the Develop module is).
Edits, Changes, Adjustments made in any other image editing software will not be read by LR.
I use the Sync folder option to update a folder that I use for PNG files I create for posting screen shots to different website like this one. But other then that I rarely if ever use that option.