If you're following the protocol laid out in the Housebreaking section -- taking your foster dog out frequently, supervising her closely, and confining her to her crate for reasonable periods of time when you can't supervise -- but you're still having trouble with potty messes in the house, there may be something else going on.
Or not: puppies under about three or four months are notoriously messy, and adult dogs may still go through rough patches when they transition to a new place. Seniors are sometimes incontinent. Stress and abrupt dietary changes can cause diarrhea in dogs. But if it's been a week or more and your foster dog really should be able to handle himself, consider whether you might be facing one of the following issues.
Is there a medical problem? Incontinence frequently signals that there's something medically amiss. One of my foster dogs, who seemed previously to be progressing nicely in her potty training, suddenly started going diarrhea not only in the house, but in her crate. It turned out she had giardia. After she started on medication, the problem vanished. Another foster dog who had impeccable potty manners came down with diarrhea after snarfing some garbage while out on a walk. A 24-hour fast cured his ills. If your foster dog starts having accidents, and especially if those accidents involve diarrhea, try a 24-hour fast to rest his digestive system, and switch to a bland diet of rice, boiled chicken, and maybe a little canned pumpkin for a few days afterward. If that doesn't do the trick, a visit to the vet may be in order.
(Note: If your foster dog is a puppy under three months of age, diarrhea may indicate something much more serious than indigestion. Sadly, many dogs are not vaccinated against parvo or distemper in the regions that WAGS pulls from. While your foster puppy will have been fully vaccinated and subjected to a 10- to 14-day quarantine before being transported north, there is still a small chance that she might have been exposed to one of these pathogens en route or after arrival. If your foster puppy appears to be in major distress within a few days of arrival, please contact your foster coordinator immediately.)
Is it submissive urination? Are the accidents limited to small amounts of urine? Are they accompanied by appeasement gestures (rolling over to show the belly, averted gaze, cowering, etc.)? Do they generally occur when you reach for her quickly, approach the dog by looming or reaching over her head, and/or seem to be angry? If so, you may be dealing with submissive urination rather than an actual potty training mistake. Do not correct the dog for submissive urination. You'll just frighten her and make the problem worse.
Submissive urination is very common among shy dogs and puppies. Fortunately, it often resolves on its own as the dog becomes more comfortable in her new surroundings. Dealing with it is a combination of management (keep the dog on easily-cleaned surfaces, try to avoid triggers like looming over her or speaking to her in a loud voice) and building up her confidence with reassurance, a structured and predictable daily routine, and positive training exercises. In extreme cases, you may also find it helpful to put the dog in canine diapers as a temporary measure.
Is it urine marking? If your foster dog is an intact adult male, or a male who was neutered late in life, and he's primarily spraying urine on raised objects or vertical surfaces, your problem may be urine marking. This is not the same behavior as house soiling -- it's driven by stress, anxiety, and/or a desire to anoint himself Top Dog and all sprayed areas as his personal fiefdom -- but you correct it in a similar fashion. If your foster dog has not already been neutered, get that done as soon as possible. Then go back to an extra-intensive version of housebreaking: interrupt him and take him outside when you catch him in the act of spraying, supervise him closely indoors, restrict his freedom when you can't watch him, and be super vigilant about cleaning up messes with an odor neutralizer, since scenting another dog's urine (or his own) often motivates an extra squirt of urine in response. Canine diapers may help here, too.