We study the fate of the surface states of Bi2Se3 under disorder with strength larger than the bulk gap, caused by neon sputtering and nonmagnetic adsorbates. We find that neon sputtering introduces strong but dilute defects, which can be modeled by a unitary impurity distribution, whereas adsorbates, such as water vapor or carbon monoxide, are best described by Gaussian disorder. Remarkably, these two disorder types have a dramatically different effect on the surface states. Our soft x-ray angle-resolved photoemission spectroscopy (ARPES) measurements combined with numerical simulations show that unitary surface disorder pushes the Dirac state to inward quintuplet layers, burying it below an insulating surface layer. As a consequence, the surface spectral function becomes weaker but retains its quasiparticle peak. This is in contrast to Gaussian disorder, which smears out the quasiparticle peak completely. At the surface of Bi2Se3, neon sputtering adds additional unitary scatterers to the Gaussian disorder of the adsorbates. Since the introduced unitary disorder pushes the surface state to inward layers, the effects of Gaussian disorder are reduced. As a result the ARPES signal becomes sharper upon sputtering.