If we exclude gain media (which emit light rather than absorb), then in most cases the problem is that absorbance is a virtual quantity which is often ill-defined as A=-lg10T, where T is the transmittance. E.g., even in case of well-diluted solutes in a transparent solvent, you actually have to define it as A=-lg10(T/T0), with T0 the transmittance of the pure solvent, otherwise strong errors can be introduced. If you use the same formula for layers on a substrate, with T0 the transmittance of the substrate, you often end up with negative absorbance, because the layer can work as anti-reflection coating. If you want to learn more, here is a review about the topic:

Article The Bouguer‐Beer‐Lambert Law: Shining Light on the Obscure

An experimental reason for seeing negative values is that the blank was not appropriate, giving a higher absorbance than it should. Make sure the cuvettes you use are well-matched (or use the same cuvette for blank and sample) and very clean.

The possible reasons are:

- Experimental conditions between measuring the absorbance of the sample, i.e. subsystem (molecules or solid state layers) of interest plus whatever comes with it (referred to as "reference", for example, solvent in the case of molecules or transparent solid state substrate in the case of solid state layers), and the absorbance of that same reference alone. The experimental conditions that may differ between the two measurements include intensity of light, stability of the sample during measurements, optical path lengths (alignment of the sample, different cuvettes, different positions of the laser spot on solid state layers etc.)

- wavelength calibration of the monochromator got displaced for whatever reasons

- the sample itself emits some light that riches the detector