Family Issues Support Group
Family issues is a huge range that go from minor conflict to major misbehaviour and even abuse on the part of individual members of the family occur. Whether you feel you are in a dysfunctional family or you're dealing with a very specific issue, this is the place to talk about it and find others who might be going through the same thing.

Do you have to live with her? Maybe consider moving out on your own? Or have you tried telling her that the way she smells really bothers you?
The smell is bacteria. It's unsanitary and unhealthy, aside from just being smelly and gross. Is she is getting treatment for her depression? You could try mentioning it to her doctor or therapist.
More immediate solutions: open windows, make sure the house and bathrooms are clean...
If the house is dirty/messy she may feel uninspired to keep herself clean. If her house/environment is clean she may feel more inclined to keep herself clean. If you can afford to, hire a maid service to come once a week or you do a thorough clean to make sure the space is clean. This might help your mom.
Tell her that if she won't do it for herself, to do it for you. If you need to, I'd say that you won't come over unless she's bathed.
Is she religious? How about having the pastor come over for weekly visits so she has a reason if you aren't a good enough one.
People often need to take baby steps when they're in this state... Your mom's family doctor or her psychiatrist could order in some Community Health help perhaps for a while to help her to take better care of herself... Help with bathing, hair washing, clean clothes etc
In the meantime she may be able to take some 'baby steps'... Perhaps you could get her some 'baby wipes' from the drug store and encourage her to have a little sponge bath at the sink .. I would treat her kindly through this There is healing to be had with some help ... Big hug...x
http://www.mayoclinic.org/diseases-conditions/depression/basics/symptoms/con-20032977
http://www.dailystrength.org/c/Depression-Supporters/support-group
Can she comfortably get into the bath or shower? Is the bathroom a clean pleasant place with a good setup??
could it be in the Mother/Son dynamic? Has it become a battle or wills? Your approach may have sparked some defiance in her and now she refuses to do it, even though she knows it's good for her.??
Is there a family friend who can talk to her, maybe invite her out for a nice girls lunch once or twice a week....and she will be motivated to clean up a bit??
Sending good thoughts your way!
It does sound like she needs help though. That's not normal. She should go in and talk to her doctor, her meds may not be working for her anymore.
She's definitely apathetic but only her doctor could confirm whether this is due to depression or there is some medical condition involved.
If you are physically living in the home with her then eventually your clothing will take on that smell so I would push to get her treated. If you are not living with her, then I would limit my visits.
She may not like what you have to say to her about her hygiene but then again, unless you push, she'll never do anything about it. It's for her own good, so I would push, push and push some more.
1. You cannot change a person who does not want to change themselves.
2. It is okay to step away and take time for yourself.
In all honesty, you can only encourage her & try to uplift her. One of the most uplifting feelings is knowing someone is there and loves you. Compliment her & let her know you love her. Redirect her negative comments with something positive. Improve her surroundings, open the blinds, light scented candles, buy her scented lotions, body wash, & perfumes, encourage her to get out & do more. When you speak to her, filter it best you can or avoid it entirely because you noted that she cries upon mention of her odor. It is at this point, a very sensitive topic for her. Also, try telling her the good things that will come if she can take better care of herself. It may not be overnight, but do all you can without allowing yourself to tire out.
I'd contact her PCP and tell him/her about the situation.