Can we do anything about a chronically smelly dog?

We’re dog sitting for my sister-in-law’s 12 year old hound dog mix. She’s a great dog, very well behaved and friendly. But she stinks! Even the day after a bath, she smells terrible. Any room the dog is in reeks after just a few minutes.

I don’t know how long we’ll have her here because we’re taking care of her during a medical emergency and things are still up in the air. I can’t change the dog’s diet (she eats Purina Beneful dog food). She does tend to have dry skin problems, but it’s nothing severe.

What can we do to make the dog less smelly? Is there any easy to find product that will be safe, or are we doomed to having a stinky house while she’s here?