The whole purpose of a fuse resistor IS TO FAIL with a massive overload. The resistor is cheaper than a fuse is why they are used. Usually that is for consumer junk that will never be repaired if the fuse fails. The choice of the resistor is that with normal operation the power heating the resistor should be far less than the rating, and with any anticipated failure the current should be enough to dissipate at least 10x the rated power in the resistor.In normal operation the circuit current will be just over 100mA resulting in a resistor power dissipation of less than 0.025W. However under short circuit fault conditions the resistor could pass in excess of 100A, which it might not be able to withstand.
I would advise the use of a fusible resistor of at least 10 ohm, which would limit the maximum fault current to less than 25A. Even with a 10 ohm resistor the normal power dissipation would be less than 0.125W. At 20 ohm the normal power dissipation would be less than 0.25W and the maximum fault current 11A.