Is a person who lives with the parent and is a caregiver, entitled to more of their estate than the other siblings?

Entitled, no. Negotiated, yes. Plans can always be reconsidered according to the circumstances. If all things considered are analyzed, possibly yes if both agree and the parent is competent and agrees. No one's opinion matters other than the two involved in an agreement.

My mother had a series of live-ins, companion care, and other help situations over time with no caregiving contracts. She was still competent and able and no one else had a say. If this had continued, she would now have no resources. When she made me poa, I saw her declining resources had to be managed more carefully and caregiving contracts were necessary so there would be no question over time. The bank manager recently commented that my mother wouldn't have been able to do this without me. Whatever 'estate' is remaining after costs of living and care will remain an accounting issue. Partly what I contributed is voluntary and by choice, because she is my mother.

I know of one brother who did caretaking for his sister regularly. When she passed, the sale of her home was split between several siblings. The brother gave his share to others more in need than himself. In another situation, I know of, the siblings compensated the caretaker sibling fairly after the mother passed.
It's possible to not have conflict.

No is the ultimate answer to me. Entitled is a word I don't overall like. Living with a parent as caregiver is a choice. It is one that my own serious limitations wouldn't allow me to make. It is up to the person giving the gift of inheritance who they wish to leave things to. And their reasons should be their own.
I DO think that it is always a mistake to move in with and care for an elder without a care contract done with the help of a lawyer. There are more costs than your time 24/7. But as I said, the choice to do it is a choice. One I would never make.
I as well would never allow my own child to care for me in this manner, thus giving up his or her own life.

As the primary caregiver for my MIL, I recently had this conversation with my BIL who came to watch his mother to give us (husband and I) some desperately needed time away. He felt that we should get everything, not that it's a lot. But I saw infighting before in this situation and feel that it should be split 4 ways (3 living children and the children of the deceased child). Honestly, I don't want any of it but it should be done like this to prevent fighting. Just my opinion.

summahjoan, there is no rule that says that a grown child who is a caregiver for a parent should receive a larger slice of the estate. It would be up to your Mother to update her Will to make the changes, if she is still of sound mind.

If it is possible for your Mother to change the Will, don't be surprise is the sibling will grumble as too many times the siblings are clueless about what is all involved when it comes to caregiving. I hope your siblings are not that way, and see the value in what you are doing.

yes mj too broad I guess, it is medicaid I was generalizing about

in my state there is a proviso where immediate family if a caregiver cannot be removed from the immediate family's house provided they lived there for 2 years prior to death.
If you keep paying the bills, there is nothing the other siblings can do to force the sale
I do not think they can charge you rent either.
I do not think they can help themselves to the use of the place either.
So, no, you don't get more, just get to remain in the family home until your death so there's that

Only if that's the arrangement made by the owner of the estate in a will or trust.

Now, whether that's fair to the person doing all the caregiving is an entirely different discussion.