I just found an article,
which reviews evidence presented in
The locations of recent supernovae near the Sun from modelling 60Fe transport; D. Breitschwerdt et al., Nature 532, 73–76 (2016),
that there were supernova explosions in the neighbourhood of the Sun (a few tens of parsecs, if I'm reading it correctly) in the comparatively recent past (about 2 million years).
What are our chances of finding the remnants of those explosions? That is: given reasonable assumptions for the parents' velocities with respect to the solar system, and for the kick given by the supernova to the remnant, how far are these remnants likely to be from the solar system now?
In addition to that, is there any chance of finding them there using current or future astronomical surveys? I imagine the answer to the latter is "definitely not", but I might as well ask. (Note, however, that the main question is where the remnants are likely to be now, and only then how detectable they're likely to be.)