To answer John Reiser's question first, yes, there are such boxes.
And to respond to DLR's concern about the line getting 'answered by the wrong machine', the point is that the _box_ answers the call and routes it appropriately. 'Distinctive ringing' from the telephone company isn't required at all.
One manufacturer is:I have been using an earlier model of theirs since 1994 and it works a treat. The one I've got has three ports -- one is connected to the phone, one to my standalone fax machine and one to the internal fax-modem in the computer (used very rarely, for dialup to the ISP if/when the broadband goes down or occasionally to send a fax directly).