Not sure if they still make them, I used to have a modem that also had Fax & Answering capability built in, and it could operate very happily without the PC live, it stored incoming traffic until the PC was powered up and ready to receive, at which point it tranferred all the relevant data to the PC, and it could then be archived, or printed, or played in the case of voice messages..
Can't remember who made it, ( I think it was US Robotics) with the change to Broadband here, I no longer have a need for fax, and mobiles have sort of reduced the need for answering machines. The other advantage is that if I'm not in, it no longer costs me to ring back