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Grounded, neutral objects gain or lose electrons by induction.

 
Case III - Negative rod/neutral object

Electrons are repelled down into the ground. Object becomes positive

Case IV -Positive rod / neutral object

Neutral object becomes negative as electrons are drawn up from the ground

Case V – Induction w/ grounded electroscope

Frame 1 - Rod comes near  

Electrons repelled down to leaves 

Total Charge?

Zero

No charge transferred

Frame 2 - Electroscope is grounded 

Frame 3 - Ground Removed,
Electroscope Maintains Charge 

Electroscope Charge?

Positive

Electrons left Electroscope

What would the charge on the the electroscope be if a positive rod were used? 

Negative