When you ask about preserving the stump, are you implying that you want it to resist decay? If so, that is not feasible, especially at this degree of degradation, and it would be a good source of recycled nutrients for the soil and any plant roots in that area of ground to let it continue to disintegrate at its own pace. Dead wood, even if just a stump compared to a standing snag, does have good wildlife value, as you noticed with the woodpecker flaking. (We'd guess it was a Pileated Woodpecker, but it's hard to tell.)

While termites can utilize stumps and old logs, they should not pose a risk to the house if they colonize this stump. They are abundant in the landscape around us, even if we don't notice them; they also serve as valued food for birds and other organisms. Plus, their activities will only speed-up the disintegration of the stump; a good thing, if you were considering having it ground anyway. If you prefer to just have it ground-down mechanically, you can keep and use the resulting wood chips or sawdust as a mulch, or add it to a compost pile if you have one. You might need to make sure the company performing the grinding has enough access through the yard (without crushing desirable plants) to get the  machine in place. We do not recommend burning it.

Miri

Thank you! Very helpful.

You're welcome!