What is 'non-detection' of a Supernova? This may have a simple answer but I can't find it. 

I've come across this term in a paper I was reading,  (Walmswell and Elridge, 2011) which mentions 'non-detection' of Supernovae, and while I can wrap my head around detection, I was lost at 'non'.

I tried finding a definition but to no avail. Would anyone be able to give one?
From a quick skim of the paper, it appears they using data from a previous paper by Smartt et al. (2009). That paper compiled a sample of observed supernovae (SNe) for which there are good images of the parent galaxies taken before the actual SNe. In some cases, Smartt et al. found plausible progenitor stars for the SNe; those are the "detections". Cases where they couldn't find a plausible progenitor on pre-SN images are the "non-detections". 

(The authors of the paper you are talking about appear to be suggesting that Smartt et al. underestimated the masses of progenitor stars because they failed to account for extra local dust extinction from the more massive red supergiant stars.)