Homopolymer adsorption and stabilization of colloids in compressible supercritical solvents are modeled with the lattice-fluid self-consistent field theory(LFSCF). Adsorption at a single surface is characterized versus bulk solvent density for various polymer chain lengths, solubilities, and concentrations. As solvent density is lowered, adsorbed chains first collapse due to the loss in solvent quality, and then expand due to an increase in adsorption that raises the excluded volume. This collapse-to-expansion transition in layer thickness occurs just above the critical solution density for a bulk polymer solution. Colloid stability is examined by calculating the free energy of interaction of two parallel surfaces coated with adsorbed polymer. Above a threshold concentration and molecular weight, the surfaces are stabilized at high density. As density is lowered, the entropically favorable expansion of solvent from the interface causes flocculation at the critical solution density of the homopolymer in bulk solution, in agreement with recent light scattering experiments. At lower concentrations, bridging occurs and stabilization is not possible, even in a high density, good solvent.