How do current and voltage relate in a power supply in extreme conditions?
This depends on the power supply design. There are many options:


Power supply burns out and never works again


This is especially spectacular with li-ion batteries -- it involves fire, explosions and lots of smoke

A fuse blows in power supply, the supply will work again when fuse is replaced
Power supply overheats and shutdowns; once it cools down enough it powers up again (and immediately shuts down again if low resistance is still present)
Power supply overheats and starts decreasing voltage, until it no longer overheats. The current stabilizes at some value which depends on room temperature, airflow, etc..
The power supply has CC (constant current) mode: the voltage is decreased to maintain exactly maximum current (so it will output 0.01A and 0.01V)
The power supply has fold-back current limiting: both voltage and current are decreased; once resistance is normal again output raises to normal levels.
The power supply has hick-up current limiting: power supply shuts off for pre-defined interval (few seconds); after timeout expires the output is restored, and if the power supply is still overloaded the cycle begins again