There are undoubtedly elastic regions of plastic material but there are very few plastics with a linear relationship of stress strain (aka Young’s modulus). This is why for most FEA, the stress strain ratio is a lookup table rather a constant for plastic material. In addition, some plastic exhibit a non-Newtonian property. Long story short , Young’s modulus is not applicable for plastic parts. Also, it is not true all solids must have a one.
You have absolutely no idea what you are talking about.
The elastic region (there can only be one) is the range where a material has a linear relationship of tensile stress and strain. Every plastic and every solid has such a region, it is part of the definition of a solid. Again, the Young's modulus is just the slope of the curve at zero, it is mathematically impossible not to have one. All but the most brittle of materials have non linear stress strain relationships, and for FEA all materials use a look up table instead of using a constant value, because that's the point of FEA. Non-newtonian behavior is completely unrelated, instead dealing with a material's stress and time relationship, and again is not exclusive to plastics.
Again, the terms plastic as in deformation and plastic as in the material are an etymological coincidence and don't have anything to do with one another.
Check data sheets for any 3d printing filament, Young’s modulus is the main characteristic in them and that's how you can reason about filament abilities.