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Abstract In this work, we employ the “horizon” function introduced by Ivanov (Int J Mod Phys D 25:1650049, 2016b) to study radiating stellar models with a generalized Vaidya exterior. Since the star is dissipating energy in the form of a radial heat flux, the radial pressure at the boundary is non-vanishing. We study the boundary condition which encodes the temporal behaviour of the model. Utilizing a scheme developed by Ivanov, we provide several solutions to the modified junction condition. We show that the presence of strings, allow for the collapse to a black hole or the complete burning of a star.