"The Bible says it is an unforgivable sin to steal from the dead. LARGE CASH REWARD FOR ANY INFORMATION FOR WHO IS RESPONSIBLE FOR THIS!!!" Duane, 66, tweeted on Friday, August 2.
The break in happened in the evening on Thursday, August 1. The thieves vandalized the store and took items that had belonged to beloved late wife Beth, 51.
Beth passed away on June 26 after a two-year battle with throat cancer.
"I cannot believe that she's gone. This is not possible. I want to wake up from a dream. In the ‘70s, I did 18 months in a Texas penitentiary, and I told God yesterday I'd do 5 years, 10 years day for a day just to kiss her again," Duane said in his emotional eulogy.
Duane has been struggling to cope with his loss. He recently revealed that he's lost 17 pounds because his grief has left him with no appetite.
Fans will see Duane and Beth's sad last days together play out on Dog's Most Wanted, set to air on WGN America in September.