How to open TIFF file created in 2001 on Mac
Most likely, the files are compressed by DiskDоubler or its equivalent. 
You can decompress it on MacOSX with The Unarchiver,
on Windows,Linux and Mac you can use unar command line utility.
You can found DiskDoubler, for example, here
I restored the 1996 year archive from Pinnacle Micro 1.3 GB Magneto Optical Disks, but could not open some files. Inside these files I found EPSF8BIM, EPSFART5, TIFF8BIM, XDOCXPR3, WXDOCXPR3 at the beginning and end, and random mess between them. I installed DiskDoubler on an old G4 MacOS 9 computer and unpacked the files, after which the files began to open without problems on Mac, Linux and Windows.
In those glorious days, disk space was worth a lot of money and people tried to solve this problem by compressing files on the fly.