Context. Determining empirical atmospheric models for the solar chromosphere is difficult since it requires the observation and analysis of spectral lines that are affected by non-local thermodynamic equilibrium (NLTE) effects. This task is especially difficult in sunspot umbrae because of lower continuum intensity values in these regions with respect to the surrounding brighter granulation. Umbral data is therefore more strongly affected by the noise and by the so-called scattered light, among other effects. Aims: The purpose of this study is to analyze spectropolarimetric sunspot umbra observations taken in the near-infrared Si I 1082.7 nm line taking NLTE effects into account. Interestingly, we detected emission features at the line core of the Si I 1082.7 nm line in the sunspot umbra. Here we analyze the data in detail and offer a possible explanation for the Si I 1082.7 nm line emission. Methods: Full Stokes measurements of a sunspot near disk center in the near-infrared spectral range were obtained with the GRIS instrument installed at the German GREGOR telescope. A point spread function (PSF) including the effects of the telescope, the Earth's atmospheric seeing, and the scattered light was constructed using prior Mercury observations with GRIS and the information provided by the adaptive optics system of the GREGOR telescope during the observations. The data were then deconvolved from the PSF using a principal component analysis deconvolution method and were analyzed via the NICOLE inversion code, which accounts for NLTE effects in the Si I 1082.7 nm line. The information of the vector magnetic field was included in the inversion process. Results: The Si I 1082.7 nm line seems to be in emission in the umbra of the observed sunspot after the effects of scattered light (stray light coming from wide angles) are removed. We show how the spectral line shape of umbral profiles changes dramatically with the amount of scattered light. Indeed, the continuum levels range, on average, from 44% of the quiet Sun continuum intensity to about 20%. Although very low, the inferred levels are in line with current model predictions and empirical umbral models. The Si I 1082.7 nm line is in emission after adding more that 30% of scattered light so that it is very sensitive to a proper determination of the PSF. Additionally, we have thoroughly investigated whether the emission is a byproduct of the particular deconvolution technique but have not found any evidence to the contrary. Only the circular polarization signals seem to be more sensitive to the deconvolution strategy because of the larger amount of noise in the umbra. Interestingly, current umbral empirical models are not able to reproduce the emission in the deconvolved umbral Stokes profiles. The results of the NLTE inversions suggests that to obtain the emission in the Si I 1082.7 nm line, the temperature stratification should first have a hump located at about log τ = -2 and start rising at lower heights when moving into the transition region. Conclusions: This is, to our knowledge, the first time the Si I 1082.7 nm line is seen in emission in sunspot umbrae. The results show that the temperature stratification of current umbral models may be more complex than expected with the transition region located at lower heights above sunspot umbrae. Our finding might provide insights into understanding why the sunspot umbra emission in the millimeter spectral range is less than that predicted by current empirical umbral models.