Fibrous cellulose materials useful in the manufacture of soft, absorbent paper products such as paper towels, facial tissues, and toilet tissue are disclosed. The paper products contain a biodegradable vegetable oil based ester-functional quaternary ammonium chemical softening compound. Examples of preferred vegetable oil based ester-functional quaternary ammonium chemical softening compounds include diester dioleyldimethyl ammonium chloride (DEDODMAC) (i.e., di(octadec-z-9-oenoyloxyethyl)dimethylammonium chloride) and diester dierucyldimethyl ammonium chloride (DEDEDMAC) (i.e., di(docos-z-13-enoyloxyethyl)dimethylammonium chloride). Depending upon the paper product characteristic requirements, the saturation level of the fatty acyl groups of the vegetable oils can be tailored. Variables that need to be adjusted to maximize the benefits of using unsaturated vegetable oil based acyl groups include the Iodine Value (IV) of the fatty acyl groups; and the cis/trans isomer weight ratios in the fatty acyl groups.