You have concerns for mom's financial future with good reason. She is adopting a lifestyle that does not take into account that her future depends on how she spends her
money now. Your concerns are reasonable and action is required. I would suggest an in-person family meeting. If you can do some forecasting for her funds over the next 10 years and put that in writing, it could be useful. Seek the advice of a financial planner if you need to, or use an accountant to figure out what she'll have left at the end of 10 years at the rate she is now spending her money. Having it in black and white on a spreadsheet can be useful if she is willing to look at that.
I would suggest an in-person family meeting. If you can do some forecasting for her funds over the next 10 years and put that in writing, it could be useful. Seek the advice of a financial planner if you need to, or use an accountant to figure out what she'll have left at the end of 10 years at the rate she is now spending her money. Having it in black and white on a spreadsheet can be useful if she is willing to look at that.
Mom may have some unresolved psychological issues, early onset cognitive decline, or a host of other conditions that could be affecting her behavior. If you can persuade her to get a checkup from a doctor to rule out any health reasons for her behavior that would be helpful also. She may need someone to manage her finances for her.
As to the future, you are not required to take mom in if she runs out of money. If she gets to the point of having nothing but social security, she will eventually become eligible for Medicaid. That will pay for a nursing home and sometimes it is the only choice for those who have no funds. If she is eligible for government subsidized housing when she runs out of money, that may be one way to keep a roof over her head, but start exploring the possibilities now. In many places, the demand for subsidized housing far exceeds the supply. I would bring this up a a family meeting, choose your words carefully, and lay out the future for her. I think you might resent having to take your mom into your home, and it's important to state your own needs and let her know that taking her in is not what you ever want to do.
If your own efforts to help mom plan for the future are not successful, I suggest getting some professional help from a social worker, elder law attorney, financial advisor or mediator to assist with the discussion. Sometimes an outside, neutral person working with you can get better results than family alone.
Ultimately, unless you take legal action as a last resort to protect your mom from herself (unlikely to succeed at this point, based on your description), she is entitled to spend her money how she wants. What happens when she runs out is going to be a consequence of failure to plan or refusal to accept advice. It can be painful to watch, but you can't force your mother to be conservative and you can't force common sense on her. Likewise, you do not have to force yourself into housing her or caring for her because of her actions. She can experience the difficulties of the elderly poor in this country if that is her choice.
"The right thing" you mention needs to include what is right for you, not just what mom may think she is entitled to getting. At this point, perhaps a choice for you is to let her know that you are not planning to take her in when she runs out of money and she is creating her own unpleasant future with reckless spending.