How long would my Niederlassungs-Erlaubnis be valid after I leave Germany and go back to my country? Does it expire immediately if I deregister myself from Germany ?

Yes it expires immediately if you unregister. Because when you unregister you will be asked to give the address to which you intend to move. If that address is out of Germany, then you are apparently shifting your permanent residence to another country which makes your German residence permit per law (AufenthG §51 (6)) automatically void on the day you leave the German soil after your unregistration.

http://www.aufenthaltstitel.de/aufenthaltsg.html#51
"wenn der Ausländer aus einem seiner Natur nach nicht vorübergehenden Grunde ausreist"

Regards,

Lacrima

Hi Lacrima,
Thank you very much for the valuable information.

What i understood from the below sentence(took from the link you provided) is that the NE will be expired if a foreigner doesn't returns within 6 months or the stipulated time(>6months??) agreed by the Ausländerbehörde. If he returns in time then it should be ok.
"wenn der Ausländer ausgereist und nicht innerhalb von sechs Monaten oder einer von der Ausländerbehörde bestimmten längeren Frist wieder eingereist ist"

How realistic is it and anyone out here had experience with "Ausländerbehörde bestimmten längeren Frist" scenario which is more than 6 months??