Min pin's are pretty high energy pups...if left alone for a good chunk of the day, it's no wonder the little bugger is acting up a bit and digging.
Having a dog of my own, I know it's a big commitment - time, energy, money. If you want to keep the dog, then that little gal is going to need more stimulation, both mental and physical, to keep her happy and healthy. Considering she's still a pup, she's bound to have a ton of energy and she needs stimulation and socialization so she can have a hope of a good life in the future. If you can't afford doggie day care (NOT cheap...I'm shelling out about $400/month for this service but it would be cheaper for a smaller dog), then there are dog walkers who can visit 1-2 times a day for walks, feeding, and play time. It's still not cheap to get a dog-walking service, but the cost is more palatable than daycare. To stimulate her mentally, there are some great "games" out there for dogs like puzzle feeders, where they have to work through a puzzle to get to their food.
If you're not able to provide these things, as much as it pains me to say this, I say find the dog another home. There are rescue organizations who can find a foster until she finds her forever home. Being a puppy and being a min-pin, she will be quite the catch and I'm sure she'll get snapped up quickly.