What would happen in this circuit?
You seem to think that you have created a problem, but not in this case. The 1A will flow through current source, there will be 1V across the voltage source. The current source will have the voltage over it that makes this happen, likewise the voltage source will have the current through it to make this happen (which must be 1A).

1A flows through the resistor too. Let's (arbitrarily) define its lefts side as 0V, then its right side must be at +100V, hence the voltage over the current source is 99V.

If you invert the current source the right side of the resistor is at -100V, hence the voltage over the current source is -101V.

Note that voltage sources and current sources are theoretical constructs, just like a line, circle and point. You can create 'impossible' diagrams with them, for instance a shorted voltage source or an open current source, or voltage sources for different voltages in parallel. It makes no sense to ask 'what would happen in such a case' because those idealized components do not exist. We can calculate with them within certain restrictions, outside those restrictions we can't calculate with them. That's all.