Usually -no. If it had it would kind of defeat the purpose of the chute.
When a parachute is deployed, the action force is the air resistance pushing against the parachute fabric. This air resistance is created by the change in the air's velocity as it passes through the canopy of the open parachute. The reaction force to this action force is the drag force created by the parachute pulling against the jumper. This drag force is created by the increase in the parachute's surface area, which slows the jumper down as they fall. The drag force is also responsible for the parachute's ability to slow the jumper's descent enough to safely reach the ground.
Capt Joseph Kittinger of the US Air Force jumped from a helium balloon at 102,800 feet. His parachute deployed somewhere around 15,000 feet - roughly the height that skydivers normally jump from.
The falling of a parachutist without his parachute deployed will be quite fast. We can slow his decsent by putting a drag on the free fall with a parachute. The fall is no longer free of drag (friction).
The force of gravity and the force of the friction of the parachute moving through the air. I can not draw a diagram on this forum.
air resistance
As long as it is not accelerating (going faster and faster, or slower and slower), the forces on the parachute are balanced. Initially, the parachute will accelerate - in this case the forces are unbalanced. It will continue accelerating, until the force of gravitation is balanced by the force of resistance.
The force that changes is air resistance and the force that stay the same is gravity.
Up thrust because the air pushes up and fills up the parachute.
"Gravity" is.
It is air resistance.
drag
force