There’s a bit you can set on a directory called the sticky bit. It makes it so a directory is “append-only”. That is, only the user who owns the file (or directory) can remove or move the file.

The man page (featured below) doesn’t make it clear, but a user also can’t edit a file owned by another user in the sticky place.

sticky — sticky text and append-only directories

A special file mode, called the sticky bit (mode S_ISVTX), is used to indicate
special treatment for directories. It is ignored for regular files. See chmod(2)
or the file /sys/stat.h/ for an explanation of file modes.

STICKY DIRECTORIES

A directory whose ‘sticky bit’ is set becomes an append-only directory, or, more
accurately, a directory in which the deletion of files is restricted. A file in
a sticky directory may only be removed or renamed by a user if the user has
write permission for the directory and the user is the owner of the file, the
owner of the directory, or the super-user. This feature is usefully applied to
directories such as /tmp which must be publicly writable but should deny users
the license to arbitrarily delete or rename each others’ files.

Any user may create a sticky directory. See chmod(1) for details about modifying
file modes.

HISTORY

A sticky command appeared in Version 32V AT&T UNIX.

BUGS

Neither open(2) nor mkdir(2) will create a file with the sticky bit set.

BSD June 5, 1993 BSD