Actually, under Linux (and other Unix/POSIX derived systems), you can move a file while another process has it open. This is because entries in directories just point to inodes (unlike MS Windows and some other systems where the directory entry and inode are the same entity).

Caveat: If the program writing the file tries to reference the file by pathname, it won't find it. For example, if the program uses a temporary name scheme that reads the directory and looks for the "highest" lexicographical name and then "increments" that, that scheme will produce duplicate names.