So I have my LED strip in my case plugged into motherboard via USB and it stays on even while the PC has turned off. I know how to turn it off in the BIOS but I am keeping it like this but I am wondering if this is any danger constantly pulling power to motherboard/USB port? Could this cause any damage since it's always pulling power?
No damage other than normal wear and tear on the leds being lit. Unless that strip is pulling more power than the usb can safely handle over extended periods.
In the USB 1.0 and 2.0 specs, a standard downstream port is capable of delivering up to 500mA (0.5A); with USB 3.0, it moves up to 900mA (0.9A). The charging downstream and dedicated charging ports provide up to 1,500mA (1.5A).
So that led strip should be in a charging rated port, or well under 0.5A @5v. Each led light uses @0.05A, so a 30 light strip will use @ 1.5A at 5v.