A bodily fluid collection system may include a canister fluidly connected to a dressing at a tissue site through an inlet. The canister may also be fluidly connected to a reduced pressure source through an outlet. At least a portion of the wall of the canister may be a membrane and may have the open edge of a flexible bag container fixed to the canister surrounding the perimeter of the membrane. The flexible bag may contain an osmotic agent capable of drawing absorbent from bodily fluid in the canister through the membrane and into the flexible bag.