My grandmother passed away last year. She had stocks with her name, my father's name, and my uncle's name. First my uncle passed, then my father, then grandmother. I was the person closest to my grandmother, however when she passed away, her funeral still had a balance. My aunt from California paid the remaining funeral expenses on her credit card. I am trying to cash in those stocks to send her what she paid for the funeral. The court gave me an affadavit of some kind to send to the company who holds the stocks. This aunt is harassing me constantly for her money (though it was not given to me, but to the funeral home.) What happens if the company will not release the stocks to me and I have to go through probate? Can she sue me for the amount she paid for the funeral?

Once, you submit the estate for probate, she has to sue the estate, not you.

But if the court gave you an affadavit, the stock broker holding the shares should sell them for you and issue you a check. Don't ask them to return the stocks, but to sell them for you.

... This aunt is harrassing me constantly for her money (though it was not given to me, but to the funeral home.) What happens if the company will not release the stocks to me and I have to go through probate? Can she sue me for the amount she paid for the funeral?

Did you agree with the aunt that you would be personally responsible for the funeral expenses? I doubt it.

Do you have a copy of the affidavit you mailed to the company (stockbroker)? Do you have proof that you mailed it? Call the company and find out how long it will be before they send you the money. Send the aunt a letter explaining that you have sent it to the company and are waiting to be paid.

It's "stock", by the way. Plural and singular forms of stock (shares in one or more corporations) are both "stock".

Did you make any kind of agreement with your aunt about repaying her the money she paid? If you did, whether it was in writing or a verbal agreement, yes, in theory she could sue you. But she would have to prove that an agreement or contract existed/ If you have no money or other chattels or other valuables she is wasting her time.
If there was no agreement she will have a difficult time sueing you though she could, since she has already paid the bill and none of the money went to you. The courts might rule that some of the money from the liquidation of your grandmothers assests be given in recompense, but that would be up to the courts.
Go and get proper legal advice.

Basically, she asked me if I would repay her. I told her that as soon as the stocks (which is the only thing left of the estate) were cashed in, that the funeral expenses would have to be covered. On the day before she paid it via phone, I called to ask her if she (being my gmothers sister) thought it would be bad of me to ask for a down grade in the burial package my gmother had chosen. She called the funeral home and verbally assaulted the director. He came in and gave me a new figure. The next day, I was on the phone trying to get my 403(b) plan to give me the money from my account to cover the expenses and she called on the other line to tell me that she had paid for the funeral on her credit card. She told me to give it back to her when I cashed in my 403(b) account. Since the funeral home now had no balance, the company holding my 403(b) denied my withdrawal request. That's when I explained to my aunt about the stocks. I never asked her for the money.

Lets get the facts straightened here. The executor/administrator of an estate is not personally responsible for the debts of the estate unless malfeasance can be proven. If the executor distributed parts of the estate before paying all its bills that could be considered malfeasance.

Funeral expenses are an expense of the estate. Generally anyone paying those expenses would be considered to have a claim on the estate. There would not need to be a written agreement, just proof of the monies paid.

So, unless you have paid out funds from the estate that should have gone to pay the funeral expenses (which generally have a high priority on claims). She can't touch you personally.

Your aunt has a claim against the estate, she was not required to pay the funeral home, it is common for them to have to wait for the estate to be settled to get full payment.

Next if you were in charge of the funeral , you did not have to ask permission to "down grade it" if the aunt asked for a higher cost funeral against your wishes, then she may be liable for the extra cost. Do not let her bully you just because she paid something she perhaps should not have paid at this point