Diagnosis
The grease is taking a wrong turn. The most common cause is the angled grease gutter/channel around the drip pan getting clogged with solidified fat or debris, forcing grease to overflow elsewhere.
How to Fix It
Let the grill cool completely. Remove the drip pan and the heat baffles. You'll see the V-shaped channel that runs around the inside perimeter. Scrape it out thoroughly with a putty knife or grill scraper, then wipe it clean. Make sure the hole that leads down to the drain tube and bucket is completely clear.
If That Didn't Work
Check the rubber grommet where the drain tube connects to the grill body. If it's cracked, misaligned, or missing, grease will leak from that joint instead of flowing into the tube.
Heads Up
This is a messy maintenance item you have to stay on top of. Letting that channel clog is the #1 reason for interior grease leaks and surprise flare-ups.