Step 1: Break the abbreviation into its four letters.
BIFR has four letters, B, I, F, R, and each one stands for one word in the full name.
Step 2: Recall what the body actually does.
This body was created to identify industrially sick companies and work out a financial reconstruction plan for them, under a law passed in 1985.
Step 3: Assign each letter its word.
B stands for Board, since it functioned as a statutory board with a chairman and members. I stands for Industrial, because it deals with industrial companies. F stands for Financial, and R stands for Reconstruction, since its job was reconstructing the finances of sick units.
Final Answer:
Putting the four words together gives Board for Industrial and Financial Reconstruction. \[ \boxed{\text{Board for Industrial and Financial Reconstruction}} \]