In case of spherical symmetry, the assumptions of finite-time formation of a trapped region and regularity of its boundary—the apparent horizon—are sufficient to identify the form of the metric and energy-momentum tensor in its vicinity. By comparison with the known results for quasistatic evaporation of black holes, we complete the identification of their parameters. Consistency of the Einstein equations allows only two possible types of higher-order terms in the energy-momentum tensor. By using its local conservation, we provide a method of calculation of the higher-order terms, explicitly determining the leading-order regular corrections. Contraction of a spherically symmetric thin dust shell is the simplest model of gravitational collapse. Nevertheless, the inclusion of a collapse-triggered radiation in different extensions of this model leads to apparent contradictions. Using our results, we resolve these contradictions and show how gravitational collapse may be completed in finite time according to a distant observer.