it is more humane to remove the extremely matted coat than to try to untangle it.
As a groomer I have seen matted dogs come to me with severe "brush burn" from the owner trying to brush out a tangled coat before their appointment.
This leads to a terribly painful skin reaction and itching while the skin tries to heal. The dogs in turn scratch at the bad skin and cause further damage.
It is extremely painful pulling out mats in a tangled coat. A toy dog has tender skin and the mats usually are around the neck, the "arm pit" areas and groin, sides...all very tender areas to any dog, but even more so to a small yorkie.
It is not as if you let the dogs coat get out of hand, it is a foster doggie, so maybe clipping her down short one time is the better option.