The only core that I have experience with is the ATTiny core by SpenceKonde. That core uses Serial on pins 0 and 1. I suppose the you could use SoftwareSerial on any pins, but I have not done so, so cannot be sure.
From the ATTiny core documentation:
On the following chips, no hardware serial is available, however, a built-in software serial named Serial is provided to maximize compatibility. This uses the analog comparator pins (to take advantage of the interrupt, since very few sketches/libraries use it, while lots of sketches/libraries use PCINTs). TX is AIN0, RX is AIN1 - This is a software implementation - as such, you cannot receive and send at the same time. If you try, you'll get gibberish, just like using SoftwareSerial.
ATtiny x5 (25/45/85)
I do not know how other cores handle serial.