Fortunately the law protects us from having anyone just swoop in and take our money. However, your grandparents might find that they are now entering a period in their life that they had saved for so wisely. If they will have any kind of in-home care or help, your family is going to be glad your grandparents have the money to pay for some or all of it. If they have health and living related expenses that are not covered by Medicare or any other public or private insurance, then their rainy day savings can now be put into service.
My understanding is that if a person goes to a nursing home, they (or private insurance) pay for it themselves, if they are able. If they are not able to pay, then Medicare plus usually Medicaid (specifically for poor people) pay for it. Some people will spend all their privately saved money and perhaps all their private insurance on their nursing home care and then that is when the public insurance kicks in. (Well except that many things are already covered by Medicare even if they are not in a nursing home.) If one person in the couple is in a nursing home, but the other is not, the Medicare+Medicaid program will leave a portion of the couple's income & assets for the one who is not in the nursing home. That is to protect the "healthy" one from having to live in the streets while the incapacitated one is in the nursing home!
Each of your grandparents could give $13,000 in 2009 to whatever number of individuals they wish. Actually they can give as much as they want to, but then you the recipients will have to pay taxes on anything beyond $13,000. (I think!) However, if your grandparents should need nursing home care
soon, Medicaid system would expect that money to be made available to your grandparents to pay for their care. You see, Medicaid is for poor (medically poor) people, but if one has money to give away, then one should have money to pay for one's own care.
Oh well, rather than try to explain so much, let me give you a readable link.
Elder Law: Medicaid Overview
Pay attention in that article to what is said about "spend down," a "look back period," and Medicaid recovering their expense from your grandparents' estates.
If you are going to make legal transfer of decision making from your grandparents to yourself or someone else (family, friend, or lawyer?), then you need to do that as soon as possible while they still have a legally clear mind to make the decision to do that. Otherwise, someone will have to go to court to be appointed some sort of legal guardian, and there would be a competency hearing for the grandparent in question---just an extra hurdle.
If your grandmother is already showing signs of dementia, it might be too late for her to empower anyone with her decision making. It depends on how far gone she is.
If she already has a diagnosis of dementia, then that might also make long term care insurance impossible to get. But perhaps it could still be bought for one of them? Who knows--maybe both. I guess it depends on how much money they have available to spend.