The Estate can do a couple different things.
Transfer the assets directly to the heirs,
or Sell the assets while held by Estate.
Either way, the Estate or the heirs get a stepped-up basis which is value at the date of death. So there will be minimal gain or loss if sold quickly.
So to answer your question, who pays the tax is the one that sells the stock, the Estate or the heirs. I have seen it both ways, however generally most sell all or most of the assets and distribute cash to the heirs, as this makes it easier.
Then the Estate file a 1041 Estate for income after the date of death.
https://turbotax.intuit.com/small-business-taxes/
Now one last thing if this a Retirement Account, it is all ordinary income when distributed versus a taxable brokerage account. A 1099R would be issued if a retirement account.
