The tyre is "detached from the wire" because I cut it open to show the fault in the construction.
The fault in the construction is that the wire bead isn't encased in rubber to glue the strands of wire together. (actually a single length of multistrand wire which passes a few times round)
So as you ride along, the wire slips and the bead diameter grows in a faulty tyre.
How does the wire go over the rim? The wire goes over the rim (in a "good" tyre) only because you put the bead in the well of the rim all the way round, except the last bit you are getting over the rim. When the bead is in the rim well, it gives you the slack to get the last bit of bead over the rim. When all the bead is on the bead seat of the rim, the tyre should be round. ....if you don't get it all on the bead seat, the tyre can have high and low spots