Long-term foster dog, poorly trained as a puppy, about 5 years old, usually goes outside to urinate but sometimes uses the carpet inside?

Small dogs have special issues regarding housetraining, I suggest reading up on that. Males are particularly problematic as new people or objects can cause them to want to reinforce their claim to an area.

I do something that my trainer and vet both raise their eyebrows at but I swear it works, I scold the pile or puddle when I find it, not the dog, I'll call the dog to me to see me scold, but the scolding is not directed at the dog at all. Then I scoop up the offending matter with paper towels and dog following along, take it outside and put it where I want the dog to go, praising the soiled towels AND the dog for being in the right spot.

As with any housetraining, immediately on waking up from the night or a nap or immediately after eating, playing or drinking take outside to go. Always always praise for going in the right spot.

Good luck...