Lawmakers are planning to hear testimony on who decides the terminally ill patient's fate when the family and doctors disagree.
The hearing in the Texas Senate on Tuesday will hear from those who want to revise the current rules and others who think the family should always decide.
Under current law, the question of whether to continue treatment goes to a hospital ethics committee if the doctor wants to stop treatment and the family wants it to continue.
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If the committee agrees with the doctor, the family has 10 days to find another hospital that will treat the patient.
Right-to-life groups are split on whether the family's desires should be paramount. Doctors say providing treatment can be unethical.
A compromise would extend the deadlines for decisions.