Does the legal guardian of grandmother have control of assets when the ward dies?

If your grandmother dies intestate (without a will) there will be laws in your state that lay out a formula of who inherits.

No it would not trump a beneficiary.

If grandmother has a will that will be how her assets are distributed. If she needs a guardian she no longer has the ability to change any of these things. If she does not, then her estate would go through probate, with a judge making the decisions about who gets what. You say no other close relatives, you will be surprised how many relatives she has if she is a wealthy woman.

I hope that doesn't change your willingness to help grandma.

No guardian is over just as POA is over at death.