A comprehensive analytical description is presented for the particle and heat fluxes collected by dust in dense magnetized plasmas. Compared to the widely used orbital motion limited theory, the suppression of cross-field transport leads to a strong reduction of the electron fluxes, while ion collection is inhibited by thin-sheath effects and the formation of a potential overshoot along the field lines. As a result, the incoming heat flux loses its sensitivity to the floating potential, thereby diminishing the importance of electron emission processes in dust survivability. Numerical simulations implementing the new model for ITER-like detached divertor plasmas predict a drastic enhancement of the dust lifetime.