Redistribute raster pixel value in underlying polygons

Given a raster layer (e.g 10km resolution) and a vector layer with many features (with finer resolution), is it possible to redistribute the value of each raster pixel in an attribute among the underlying polygons, so that the sum of that attribute in the underlying features is equal to the overlaying pixel value?

If so, can this be done either homogeneously across underlying features, or based on a weight given by another attribute in the polygon layer?

QGIS-based solutions are favoured.