Belgian authorities should not have any problem with you exiting the Schengen except sometimes making sure you are not overstaying. Assuming you are Indian citizen, and thus need a visa or permit to be in Schengen, you might be subjected to additional screening to assure that you were lawfully in Schengen, which a copy of card, Police Report, and few others (any marks/stamps on your passport, any job/study/how-you-was-resident, utility bills, any documentry proofs) should suffice.
Once you reach India, those authorities are concerned only with your passport, making sure you can enter India (and luggage if custom). They do not care how or why or from where you came from, except for statistics, and your identifying you as Indian with passport is enough.
Coming back to Schengen is complete different story. First you have to convince the airline to let you board flight, and they most probably will not accept a copy of card (or Schengen Police Report, utility bill, anything short of Residency Card or Visa along with your passport). They are on the hook for hefty fines and penalties in case they bring a person who doesn't have proper entry documents. A copy of your card might convince Schengen Border guard (or any country) that you are lawfully resident, but only if he/she is willing to go full lengths to check your story by database, phone-calling. And so thus, airlines will not take risk by boarding you.
Note that this above is not specific to Schengen, but to any border. An American citizen can easily approach American Border posts from Mexico or Canada without passport, and most probably they will let him/her in after they verify that he/she is indeed an American citizen. But same person can never board a flight to America because airlines have no way/means to verify his/her status based on his/her verbal story, which a CBP guard might have.
Ideal solution is to get the card before you exit, or get all relevant proofs (police report, job/work/house/copy) and get something from German embassy in India, a temporary one time use entry or a duplicate card or something.