My sister lives on the other side of the country from me and while we've never been close I am all the family she has. I am married and we have 4 grown children. My sister is divorced and lives alone. We always include her in our holiday get togethers and other than that we may visit her once a year at the most. I doubt if she will be able to travel to join us this Christmas. Our family has all noticed a decline in her memory and ability to manage simple tasks over the past few years but about a year ago when her special guy friend died things began to get much worse. She is easily confused. She can't manage her checkbook, asks neighbors how to write checks. When I was recently visiting she asked to help and yet couldn't manage to set the table. I'm quite certain she can't manage the stove or the microwave. She let me do all the driving while we were visiting and gave me accurate directions to all the places she routinely goes, in many cases telling me more than one way to get there. Many of her neighbors have contacted me with their concerns. When my husband and I and a wonderful friend tried to gently suggest she see a doctor, she got very aggressive saying that she felt ganged up on and refused to discuss any kind of support. She has resources that would allow her to stay in her home with proper support but she refuses to see a doctor. She has told us that she already did so and he said there is nothing wrong. I am fearful that she will get locked out of her house, or get lost and yet I have no clue how to help her. I am quite certain she is very scared as both of our parents suffered from dementia. But burying her head in the same is not helping. She has always been difficult and not a particularly nice person and really has no BFF. Even her friend who has been amazing in the support is doing so out of sense of "what's right" not because she cares for her. Everything I read is about how to help a parent with dementia. I'm not willing to be responsible for her care but I do want to help her get the help she needs.
You could do worse than contact social services in your sister's area - look them up online - and outline her situation to them. If they agree there is cause for concern and want to follow it up, perhaps you could also get the kind persevering friend and/or a close neighbour to agree to liaise with them. But keep the communication chains short or it'll end up being a right pig's breakfast.
Your sister's situation is very sad but the key factors in that sadness are her loss of her partner and her tendency to self-isolation. Neither of which is really curable. It's a case of accepting what you can't change, while keeping alert to any practical help you might be able to contribute.
How old is your sister, by the way?
But back to your original question: how to help your sister who has dementia? Countrymouse had a good suggestion in that you can call Adult Protective Services in her area, get her into their system. They will most likely send out a social worker who will do an assessment if they take her case. However it might depend on your sister's age but it wouldn't hurt to find out.
How much do you want to help your sister and what kind of help are you able to offer since you two live so far apart? If she's lucid and refuses to see a Dr. there's nothing you can do about that. She has a right not to see her Dr. You may have to wait for an incident before you are able to understand the full scope of your sister's memory problems. An incident being a fall (again, much of this is dependent upon her age), a kitchen fire, she wanders off and the police get involved, etc.
She's not going to be upfront about her health and if she's going to hide it (out of fear or embarrassment) there's nothing you can do right now to help her since you can't even determine what kind of help she needs.
Maybe you can plan a visit for the sole purpose of seeing how she's doing, to get an idea of what's going on. Snoop around her house. You're looking for spoiled food in the fridge, unopened mail and bills stashed out of sight, used toilet tissue in the bathroom trash can, the general upkeep of her home, and how she looks to you. Is she clean and tidy or does she look disheveled and dirty?
You might be at the beginning of a very long road.
A big concern is your sisters finances. She can easily be scammed or mismanage her funds and be left with nothing in short order. By the time local authorities get involved she could be wiped out.
If you're up to it, you might try to intervene, get her to grant you poa or see a lawyer about guardianship and get control of the funds. She's going to need money for her care. From what you describe this is going downhill pretty fast.
Of course this would take some work, a trip to visit and she may not be cooperative in granting you poa. But at least you could coordinate her care with the local authorities.