How dangerous is induction in my wires?

This is not an induction effect. Your meter is not faulty. It is possible for significant voltages to be present between the neutral line and true ground in the absence of significant current flow in the circuit because of what else is connected to that neutral and how much current those things are drawing. This is a matter best discussed with a trained electrician.

If the wire is not connected to anything, it is a floating wire and the voltage measured on such wire would depend on parasitics.

More specifically, there is some parasitic capacitance, $C_{fh}$, between the floating wire and the hot wire, as well as some parasitic capacitance, $C_{fn}$, between the floating wire and the neutral wire.

When you connect one probe of the voltmeter to the floating wire and the other probe to the ground, a voltage divider is formed between the hot wire and the ground and this voltage will be divided between $C_{fh}$ and $C_{fn}$ in parallel with the input impedance of the voltmeter.

The outcome will depend on the type and length of the cable and on the input impedance of the voltmeter, but you can easily measure some significant voltage there.

It is also possible that the cable is faulty ($140$V seems rather high), so don't make any assumptions without careful testing.

You can find some more details on the topic in this post on the home improvement forum.

It does sound like you are seeing induced voltage here, which is very commonly seen with house wiring when measured with a cheap multimeter. It's often called "phantom voltage." It will disappear if you connect the smallest load to it, and therefore is not dangerous.

Better meters for house wiring and other electrician type tasks have a low impedance (low Z) voltage test, in which the meter itself has low enough impedance that it will make these phantom voltages vanish. The meter itself is enough of a load to make the induced voltage disappear.

Old fashioned solenoid voltage testers and most analog meters have enough impedance to keep you from getting fooled by induced voltages. If you're going to work on house wiring, I'd strongly suggest a combination of a non-contact voltage tester and a solenoid type voltage tester, used properly these will keep you safe and give you enough info to troubleshoot.

This low Z test would not be desirable feature in some electronics work - in a delicate circuit with tiny working voltages the current the meter draws could disrupt the circuit you are testing.

There may be another problem here - it appears from your question that your ground wire is floating - that is it is not connected to anything, not bonded to the grounding system - and depending on the electrical system where you are, in most that green wire should be grounded properly for safety, but that's another question.