The directory entry is just a pointer to an inode. The inode contains the meta-information about the file (other than the name), and pointers to the file's data (if any). When you start to copy a file you get a handle to the inode.
The operating system maintains a count of references to the inode. As long as there are references to the inode, the inode and the file's data are kept. Once all references to the the inode are removed, the inode is and the space required by the file is released.
As you have the file open for copying it will be kept until your process closes the file. This should occur when the file transfer finishes, and will happen if the copy process fails. If the file transfer fails part way through and you have deleted all hard links to the file, you will be unable to successfully restart the transfer.
EDIT: As other have noted, file moves on the same device are done without moving the data. Instead a new directory entry is created in the destination directory, and the original directory entry is removed.
It is possible to have multiple directory entries for the same file. These are called hard links. They are created by making a new directory entry for the file without removing the original entry. The file system's inode has a reference count to record the number of directory entries pointing to the file.
EDIT2: If the process crashes or is killed, the file will be cleanly removed as the in memory access count will be reduced to zero. This is the action that occurs when the the program ends normally.
In the case of a power fail or other unorderly system shutdown, the disk will need an
fsck (file system check) before it can be fully mounted. Depending on the state of the on-disk inode and directory structures, the space will be recovered, the file will remain in the directory, or a new entry will be made in the
lost+found directory. The results will depend on which changes have been flushed to disk or written to the file systems journal.