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The description sounds like a mild colitis...what happens is the initial part is firm and ready, but the remainder of the stool has not been appropriately "prepared" but the bowel evacuates anyway.
Many times this can be controlled with a better food. At 8-10 yrs of age, the dog should be on a senior diet. My recommendation is Eukanuba Senior. The senior foods are balanced more for an aging dogs GI tract...to include more fiber for better help with bowel movements. Since your dog is not clinically sick...I would start with this change. Change the food over 2-3 days of mixing. The other thing is if it continues or you see more straining to defecate...you need to have his prostate checked.