How to keep animals from digging under the ground and rotting trees?

Brenda I’m so sorry about this issue. Can you build a boarder around the base of that tree? I don’t think mulch will help. Maybe a brick circular base? Or maybe heavier rocks? Darn animals!

Try sprinkling "Blood Meal" around the base. Generally the smell deters them from digging.

If it's neighborhood cats and dogs, you can sprinkle cayenne pepper to deter them , or Rue essential oil sprayed liberally. Castor bean plants grown nearby will deter ground hogs. You can also liberally spray the area will agricultural grade castor bean oil.

Squirrels are deterred with Thiram and cayenne pepper mixed with garlic.

If you dig a shallow area around the lilacs and spread moth balls (crushed and whole), it may deter digging. Cover the area and sprinkle more moth balls.

I'd wonder why the animals are choosing to tunnel in an area filled with roots. Where I live we don't have groundhogs so I don't know about their habits but we do have squirrels, moles/voles, & chipmunks. It doesn't sound like a area they would choose for digging unless the area contains a food source not available elsewhere in your yard. In that case, eliminating the food (grubs maybe?) might help. I'd also wonder if the rotting happened first and is supporting a food source & then the rotting has worsened because of the digging.

Be careful using mothballs if you have pets or small children. They are poisonous.

Good luck!