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The lifecycle of dust in the interstellar medium (ISM) is heavily influencedby outflows from asymptotic giant branch (AGB) and red supergiant (RSG) stars,a large fraction of which is contributed by a few very dusty sources. Wecompute the dust input to the Small Magellanic Cloud (SMC) by fitting themulti-epoch mid-infrared spectral energy distributions (SEDs) of AGB/RSGcandidates with models from the {\em G}rid of {\em R}SG and {\em A}GB {\emM}odel{\em S} (GRAMS) grid, allowing us to estimate the luminosities anddust-production rates (DPRs) of the entire population. By removingcontaminants, we guarantee a high-quality dataset with reliable DPRs and acomplete inventory of the dustiest sources. We find a global AGB/RSGdust-injection rate of $(1.3\pm 0.1)\times 10^{-6}$ \msunperyr, in agreementwith estimates derived from mid-infrared colours and excess fluxes. As in theLMC, a majority (66\%) of the dust arises from the extreme AGB stars, whichcomprise only $\approx$7\% of our sample. A handful of far-infrared sources,whose 24 \mic\ fluxes exceed their 8 \mic\ fluxes, dominate the dust input.Their inclusion boosts the global DPR by $\approx$1.5$\times$, making itnecessary to determine whether they are AGB stars. Model assumptions, ratherthan missing data, are the major sources of uncertainty; depending on thechoice of dust shell expansion speed and dust optical constants, the global DPRcan be up to $\approx$10 times higher. Our results suggest a non-stellar originfor the SMC dust, barring as yet undiscovered evolved stars with very highDPRs.

The evolved-star dust budget of the Small Magellanic Cloud: the critical role of a few key players