Would like to know powers of POA. Can the POA do this?

If the Canadian laws are close to US laws, then if there's no will when she passes her estate goes into probate. That is, whatever the PoA didn't use (or sell) on her behalf to go towards her ongoing care while she is alive. If funds from her home in India are needed to pay for her care, then so be it and no one should give the PoA any grief about this decision.

Expectations of inheritances cause all sorts of problems within families and drive them to make poor decisions regarding financial management of the elder's care and affairs. It would be best for your sister's family to have NO expectations of an inheritance (aside from the beneficiaries of the bank accounts). Then, if anyone does receive anything after that, it will be a pleasant surprise to them.

As said, POA stops at time of death. If no Will, then someone needs to go to Probate at time of death and be assigned administrator of the Will. This person does what an Executor does but...the State (in the US) determines who inherits. If a Spouse, a % goes to them and a % to the children if any. If no Spouse, it all goes to the children.

At this point with moderate Dementia, she may not be able to assign a POA or make a Will because she needs to be able to make informed decisions and understand what she is signing. With a beneficiary, if she has only assigned one to each acct, that person is not obligated to share it with anyone. Its their money to do as they please. Same with insurance policies. Beneficiaries do not have to share, they also don't have to pay for funeral expenses unless targeted for that reason.

The house in India, I agree that it will cause problems but...that really is not your problem. Sorry if I seem a little rude. If there are children, then at her passing, they will have to deal with it. Because Mom has no POA or Will they need to know how the laws where she lives works so they have no surprises. If you sister is suffering from Dementia she probably eventually need to be placed in an Assisted Living or Long-term care facility. If that happens, then her money will be used for her care so there maybe none left when she passes. The only thing that can be done now is for someone to become her guardian and it should be one of her children. Preferably the child that is willing to be the Caregiver. If you r the Caregiver, than maybe u. But then again, that stops at death. Not having a Will is your problem.

I think the key problem here is that you fear her children fighting over the inheritance; if they are inclined to do that then the only preventative would have been for your sister to have written an iron clad will and unfortunately it's much too late for that.

If she's designated beneficiaries for her money, then she's basically made a will. She's decided who gets the money. If it's the kids -- fine. If it isn't, then she didn't want them to have it.

As for a house in India, well, I wouldn't want to touch that with a ten-foot-pole. Dealing with overseas real estate could be a nightmare.

thank you for your answers.

There is so much that you don't understand here that I would suggest you pay for an hour of time with an Elder Law Attorney. You will need a family meeting to discuss your options. And do understand that I live in the USA so what I say may or may not pertain in Canada by your own laws.
First of all it is likely way too late for a POA to be done. They can be done by competent people only who understand exactly what they are doing and the document itself, as drawn gives powers to the person according to the wishes of the person appointing them POA. Then there are Fiduciary LEGAL duties of the POA to operate within the law, to do nothing that could enrich themselves, to keep meticulous records of every penny in and every penny out. Because it is likely too late for POA you are left with guardianship. That is a more complicated legal process that must go through the court. The guardian would act in place of a POA. The guardian would decide all things including placement. Both guardianship rights and duties and POA rights and duties end with the death of the person.
IF accounts have a POD listed (pay on death) then that account goes to the person designated as POD. BUT if they distribute that money to other people that is purely their own business but WOULD HAVE, at least here, tax repercussions to themselves. If there is no will in our country the person is considered to have died intestate, and their estate would go to the court where a probate would be open and an executor assigned to divide the state according to the laws of that state. The executor would pay all bills owing to the estate, and then do the division according to the laws of the state, by percentages dictated by law. The home in India would become a part of the estate. If no one in the family is capable of handling this clearly complicated estate the state would appoint an executor who would be paid, a fiduciary, some percentage of the state to manage it and to distribute it.
It is all very complicated, and as I said, what I have told you applies in this country. I can't speak for your own. So you need expert advice.

As bundleofjoy stated any POA ends the minute the person whom the POA was for dies, so they will have no say over what goes where and to whom at that point. And the purpose of having a POA is to ensure that the person who it is for, is well taken care of and the right decisions are being made regarding their health and finances.
Sounds like perhaps her family might want to talk to an elder law attorney to see what if any their options are at this point. Best wishes.

POA ends the moment she dies.

i wish her well, a long and happy life.