An annular safety valve that is positionable in a wellbore may include a housing having an opening extending through the housing to allow to allow pressure to transmit between a first annular area of the wellbore below the annular safety valve and a second annular area of the wellbore above the annular safety valve. The housing can define the opening by a seat face. A poppet may extend through the opening. A groove may at least partially surrounding the seat face for maintaining a shape of the seat face in response to an increase in pressure in the first area of the wellbore. The shape of the seat face may correspond to a surface of the poppet for preventing pressure from transmitting between the first annular area of the wellbore and the second annular area of the wellbore when the annular safety valve is in a closed position.