If bought online you can reprint a copy. If purchased from a vendor here's the instructions from the Fishing Regulations:
STOLEN, DESTROYED LICENSE
REPLACEMENT:
1. Vendors cannot issue a duplicate license.
2. Obtain an Application for Duplicate License or
Permit from a vendor or IDNR office where licenses are sold.
3. Mail completed application plus $3.00 fee . to: Illinois Department of Natural Resources
License Section
P.O. Box 19459
Springfield, IL 62794-9459
PS ; If it was a 2011-2012 license buy a 2012-2013.