Semiconductor material is having one to two electron volt energy band for electron to come into conduction band to form the conduction, in material. Which needs the potential difference, between ends, to energized, not the polarity respect to ground zero. Hence thiristor will worked normaly, as the needed potential difference, according to manual are achieved( anode is at 20 volt higher than cathode raferance.).
When a thyristor turns on the voltage across it become zero. But when you apply negative voltage across it, it goes into reverse biasing mode. The outer junctions J1 and J3 become reverse biased mode.... current falls abrupty and device gets turned off. you can verify this using simulation.
It's not simple because thyristors respond to both voltage and rate of change of voltage. The "on" voltage drop is not zero. Each junction drops a voltage roughly proportional to the log of the current - typically 1/2 to 3/4 volt. Since I don't know what you plan to do with the device, it's ratings, etc, best read the manual. Radio Shack used to carry some decent simplified books on the devices.
If you apply a voltage source of -20V at the anode of a SCR with respect to the circuit ground, and also apply a voltage source of -40V at its cathode, then heavy current will be drawn from the sources through the SCR since the SCR voltage drop will be low in the present ON condition, somewhere around 1.5V and hence cannot support a 20V difference without drawing heavy current (theoretically till its forward drop builds up to 20V or till the applied 20V voltage drops down due to its finite source impedance !) Undoubtedly the SCR will remain ON as it is still forward biased, irrespective of its voltages with respect to circuit ground, since the SCR appears to be floating with respect to the circuit ground potential.
It is said that, for a thyristor to conduct (after it is triggered), the anode must be at a higher potential, or it must be more positive, than the cathode.
Relating to the above fact, will not the thyristor work normally? or is there something else to be considered?