MHD models and the observation of accretion streamers confirmed that protostars can undergo late accretion events after the initial collapse phase. To provide better statistical constraints, we study the evolution of stellar masses in MHD simulations of a $4$ pc$^{3}$ molecular cloud. Tracer particles allow us to accurately follow the trajectory of accreting material and thereby constrain the accretion reservoir of the stars. The diversity of the accretion process implies that stars in the solar mass regime have vastly different accretion histories. Some stars accrete most of their mass during the initial collapse phase, while others gain $>50 \%$ of their final mass from late infall. The angular momentum budget of stars that experience substantial late infall, so-called late accretors, is significantly higher than for stars without or with only little late accretion. As the probability of late infall increases with increasing final stellar mass, the specific angular momentum budget of higher mass stars is on average higher. The hypothetical centrifugal radius computed from the accreting particles at the time of formation is orders of magnitude higher than observed disk sizes, which emphasizes the importance of angular momentum transport during disk formation. Nevertheless, we find two key results that provide an intriguing explanation of observed disk sizes. First, the centrifugal radius is highest for stars with substantial late infall, which strongly suggests that very large disks are the result of recent infall events. Second, there is a subtle, yet visible trend of increasing centrifugal radius with increasing final stellar mass in agreement with observed scaling of disk radius and stellar mass. Finally, we show that late accretors become more embedded again during late infall. As a consequence, late accretors are (apparently) rejuvenated and would be classified as Class 0 objects despite being $\sim 1$ Myr old.