How safe is my soldering iron?
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1 unearthed and, 2, earthed.

You are correct to be concerned. If a wire comes off the element or the insulation breaks down the case may go live. In the circuit of Figure 2, if enough current goes to earth the fuse will blow. An RCD or GFD will also offer protection.

Get a better iron.