Connect fingerprint sensor to serial PC
If I understand correctly, you are using a USB to serial cable to connect your fingerprint sensor to the PC.
If the cable is using the +5V USB (PC side) supply (to drive it's MAX232/FTDI IC or whatever it's using), then for it to receive data from the sensor, it only needs the TX/RX and ground anyway, so it should work just fine as long as the two have a common ground (i.e. the cable ground and sensor ground are connected)    

If I have misunderstood things, it would help if you could provide a link to your cable/datasheet.