Molecular clouds have inhomogeneous density profiles and have been observed to be `clumpy' in nature, containing dense cores, rarefied filaments and cocoons. Energetic mass-ejection phenomena created during the gravitational collapse of dense cores are thought to be responsible for the molecular outflows that are observed in molecular clouds. Interactions between these molecular outflows and the inhomogeneous molecular clouds they encounter may cause changes in the observable characteristics of the outflows by affecting their velocity structure and morphology. Consequently, in this work, we aim to gain an understanding of the consequences of a relaxation of the usual assumption of a homogeneous molecular cloud or ambient medium, that is normally made in numerical simulations of molecular outflows. In particular, we simulate outflows propagating into inhomogeneous molecular clouds of decreasing density, i.e. outflows in the process of leaving their parent molecular clouds. We would expect such flows to appear severely truncated in CO emission maps, in comparison to their full flow extents. Using various prescriptions for inhomogeneous media to create more realistic density profiles, long duration numerical simulations are run. The simulations include the use of an improved cooling function the effects of which we describe. Standard observational methods are used for inferring the average outflow velocity and outflow age from the simulations. We examine the effects of the different density profiles on these key parameters and on the density structure, mass-velocity relations and length-to-width ratios that characterise the outflows.