Fusible link

What is the symptom? Ford used three or four different starter circuits. Are you referring to the relay on the inner fender by the battery, or do you have one mounted on the starter motor?

What is happening to it?

That is absolutely not possible. A fuse link is just a piece of wire, but it's slightly smaller than the rest of the circuit it protects, so it's the weak link in the chain, so to speak. If the solenoid is shorted, that will burn out the fuse link wire. More commonly, you have the wrong solenoid. There are three versions that vary by year and transmission type.

You still didn't tell me what the symptom is. Also, what is the history that led up to this? Can you figure out where the fuse link is connected on each end so I can find it on a wiring diagram?

Does it make a single, rather loud clunk each time you turn the ignition switch to "crank"?

Do you have a test light and know how to use it? If you do, and if the solenoid does make that single loud clunk, use the light to test for 12 volts on the two large studs on the solenoid. One will have 12 volts all the time. The other one should have 12 volts when the solenoid turns on. If you DO find 12 volts on the second stud, a real common suspect is the strands of wire are corroded away under the insulation, right next to the terminal that is bolted to the starter motor. To verify that, test for 12 volts down at the starter. If it's missing there, or low, suspect that cable.

I'll be back tomorrow to see how you're doing.