Unsupportable...thats what you are....

With apologies to Nat King Cole :)

Database backup failing

Write on "D:\backup\MyDatabase\MyDatabase_20150208104103883_D.bak" failed: 665(The requested operation could not be completed due to a file system limitation) [SQLSTATE 42000] (Error 3202) 

Hey, customer...let not put backups on O/S compressed drives please.

Oh...and why do you have your MDF/LDFs on the same drive...also compressed?

Resolution - punt it back to them and tell them SQL Server on compressed drives is unsupported config by Microsoft and by me.   Uncompress and expand or add a drive and uncompress.

Sheesh.  How many worst practices can you get in one server?