I lost my Indian passport in India. I have applied for a new one. Inside I had a valid Schengen visa that expires in April 2017 from the Dutch embassy. Can the embassy issue a copy of the same visa to me on the new passport?
According to VFS Global (the company that handles Schengen applications for many consulates in India):
What do I have to do if I have lost or misplaced my Indian passport with a valid Schengen visa?
You are strongly recommended to keep photocopies of your passport’s data pages and of the Schengen visa. A visa is a valuable document. Inform The Embassy / The Consulate from where your visa was issued immediately if you have lost your passport. You must apply for a new visa by submitting all documents and payment of visa fees. You must submit a copy of the Police First Incident Report (FIR) with your application. It is preferable to also submit a copy of the visa and the lost passport for ready reference of the Visa Officer.
So the answer is that you should apply for a new visa with a police report about your stolen passport.