What happens after opamp saturates
Undefined and varies between opamps. 

You may see voltage on the supposedly virtual earth input. If that voltage exceeds the supply, (or some lower voltage relative to the +ve input) there may be protection diodes to drain the excess current.

You may leave one or more stages inside the opamp saturated, and saturated transistors turn off slowly, ruining high speed opamp's performance.
Therefore after the excess input current is removed, it may be a long time (microseconds) before the opamp correctly responds to input signals again.

If this behaviour matters to you, it needs to form part of your criteria for selecting an opamp, in discussion with the supplier's application engineers.

But the correct answer is : it won't happen, because you'll re-design the circuit to avoid saturating the opamp.

EDIT: From the datasheet which should have been linked in the question : 


  Input Protection
  To
  prevent
  breakdown
  of
  internal
  devices
  in
  the
  input
  stage
  , 
  the two op amp inputs should NOT be separated by more 
  than
   2.0
  V. 
  To
   help protect the input stage, internal circuitry 
  will engage automatically if the inputs are separated by 
  2.0V and input currents will begin to flow. In all cases, 
  care should be taken so that these currents remain less 
  than
   1
  mA.


So, with the positive input grounded, if the illumination saturates the amplifier and Vin- starts increasing, the device is in danger of breakdown when the input reaches 2V, at which point the photodiode is still reverse biassed by 3V. Then protection can absorb an additional 1mA, before the input voltage rises further. 

While @le_top is correct that once the photodiode becomes forward biassed it will start to absorb any excess current, it's quite clear from the datasheet that this specific opamp won't survive to that point.