A dog who self injures?

Yes that can happen,  some times a skin condition (for whatever reason) and anxiety will result in such.  So, will anxiety alone although that is more likely   a licking behavior versus a chewing behavior.  A trip to the vet is a must or infection and additional sores will likely occur.

I honestly don't have answers, I think dogs do get anxious and start licking or biting,,,,but mainly I want to just say "bless you for caring for this dog and taking over watching it!!"

It's very likely that this dog has allergies - they may be seasonal since they come and go.  Dogs don't "self-injure" as people do for pscho-somatic reasons (i.e., not out of self-hatred) but rather because the histamines that rise to the surface of the skin cause intense itching -- then once started, just the stiffness of the saliva-soaked hair will cause itchiness -- it literally becomes habit and a sad dog is likely bored out of his mind.
 
I don't think you are crossing a line at all -- if it is at all possible, why not suggest you take the dog since these folks obviously don't enjoy it. 

Thanks for all your input in helping me understand what could be wrong with her.

The information i gave you was probably confusing and a little brief so here goes, as far as i know in terms of breed shes a mixed breed but most likley half german sheperd, shes about 8/9 years old and has a good nature. I live in Hong kong, and i live in a sort of compound, there are two other houses, basically this dog belongs to very good friends of mine that left the country however their parents were still living here and would take care of the dog, but these days the parents are spending more and more time with the children in the Philipines, so the cousin of my friends now works for a family that live in the other house, to be honest i dont think shes abusing the dog but rather not educated enough in their needs. She is a Philipina and no disrespect to her or any one else, but i know that in many Asian countries animals are not really cared for too well, she is fed and she has enough water and shelter but i think she lacks love and attention.

In saying that this caretacker is not educated in the needs of an animal i am not being racist as i have grown up and lived my whole life in Hong Kong i see people treating  animals worse then we would in the west simply becuase of a lack of education. To be honest i think its becuase shes bored and lonley.

Thanks again for all your help.