These things are considered and the options weighed.
That is, what is the threat to the aircraft & other occupants versus the risk to the person have a medical problem.
If there is a real threat to the continued safe operation aircraft (such as both fuel lights coming on - Hawker) is greater than the risk of damage landing over weight then the landing will be done ASAP.
If the touch down can be kept to less than 600fpm, there should be minimal or no damage.
However, the aircraft will need an inspection and thus it's grounded.