Looking at this fuse, in-between the two main posts is a fine wire. When this fine wire gets overheated it will melt. If you put a probe on one post and a probe on the other your continuity tester will not beep.
I have no idea what you are talking about. Continuity has been broken. With the fuse still being in the fuse holder there is enough sticking out of the
back that you can touch with the probes. You DO NOT have to remove the fuses to test them. Started wrenching in 1972 and this method has not failed
me yet. Used it with the glass fuses as well. Do you understand the word continuity? We are testing to see if power is going from one side of the fuse
to the other, not how much power is in the circuit.