I have a laundry sink made of what looks like concrete in my basement.
The house is about 50 years old, I don't know if the sink itself is
that old.

Under the sink, there is an small extension where the drains are
located. This is the rusty-looking thing at the top of the picture in
the URL below.

There is some kind of bushing which is screwed into this extension
into which the drain pipe is inserted that prevents water from running
onto the floor (this is the white thing on the left of the pipe at the
top).

This bushing, which I think is made of rubber, is deteriorating and
has broken off on the right side of the pipe, so that water is running
out from a crack between the drain pipe and the extension under the
sink -- not a lot, but enough to be annoying.

Does anyone know if this bushing is some part which is still
available? I have checked a few online sites for information, and
can't find anything...

http://www3.telus.net/~mjq/sink.jpg