Can a star be massive enough to go 'supernova' yet not be massive enough to leave behind a neutron star? Or, perhaps vice versa?
This diagram from the Wikipedia article on supernovas mostly answers your question I think.

There is in fact an interval that is expected to not produce a remnant, but it is not at the lower end of the mass range, interestingly. Instead it's a result of the particular mechanism that triggers the supernova for these heavy stars, which blows the core apart entirely.