That part is a 0603 size 2Amps ferrite bead.
It also surpresses noise, but the main purpose of it in this circuit is to fuse out if too high current is flowing into the circuit, so the internal circuit and parts will not blow up.
The type number of the ferrite bead is CB03YTYH151 :
https://lomex.hu/pdf/(vik)_cb.pdf
If more than 2Amps is going into the circuit via the power supply + input for some time then this part burns/fuses out.
So, the question is if something was just temporarily overloaded, e.g. an output was shorted out and that caused the ferrite bead to burn out or if it burned out because something else damaged on the HDBB2 which is now in short circuit.
The board can work without this ferrite bead (removed and 2 pads bridged with a wire), but if something is in short circuit on the board then that may burn out other things on the board if you will repower the circuit with the ferrite bead fused, because then there will be nothing which will fuse, but the weakest link will fuse which may be a trace on the board or an IC leg etc.
My advice is to place a bridge in place of the ferrite bead and without anything connected to the board try to measure resistance between the power + and - inputs.
If you see no short on the measurement then try to power up the board, then the chance is very little that there will be a problem.