LP2985A - what's the exactly state when the ldo en is pull down(ldo is shutdown) ?

This depends on which LDO you are talking about.  But in general, it means that the pass element is off (open).  If the pass element is a MOSFET, the body diode will still conduct reverse current, of course, since it cannot be disabled.

just like lp2985a , if I put the on/off pin  low ,the output is what?

thank you for you answer . I want to control the power. I need LDO has no output at first, when at a proper time , I put the on/off up then the power will be added.  right?

Yes, when the On/Off pin is low, the IC will be Off and when it is high the IC will be On.

if I need the statement is steady,should I connect  a resistance to GND ?  (pull down resistance)  how large is the resistance value?  thank you

I do not understand your question.  Can you re-phrase it?

There is an internal voltage divider in the part from Vout to GND.  This will pull down the output voltage when the part is off.

sorry，I mean when I  use cpld/fpga control lp2985 so I need connect on/off pin to a resistance to ground ,so it can insure lp2985 is shutdown. right?

Yes, a 10k resistor can be connected from On/Off to ground to keep the regulator off.  Then, the output of your uC would be connected to the On/Off pin and would need to be active high to turn on the IC.

thank you very much