What does "turned over" mean? Did sister actually make a gift of the shares to someone -- as in, actually transferring ownership? Whose names are the shares in now? If sister actually made a gift of the shares, she needs to file a gift tax return.
One way or the other, it depends on what sister's cost basis in the shares is, how long the shares have been held (more than a year or less than a year), and what tax bracket the actual owner is in when the shares are sold. Cap gains tax is owed on: Net Sales Proceeds minus Cost Basis. If the shares sold have been held for less than a year, the gain is short-term and taxed at ordinary income tax rates. If held for more than a year, the gain is long-term and taxed at either 5% or 15%.
For what it is worth, if sister is in danger of passing away, a better strategy may have been to dispose of the shares in her will or putting a designated beneficiary on the brokerage account or adding a co-owner as joint tenant with right of survivorship. When someone acquires assets as a beneficiary of a decedent, the cost basis is "stepped-up" to the value of the asset on the decedent's date of death.