Binary pairings that haven't been discovered yet? Question: Are there any kinds of binary pairings that haven't been discovered yet? Any that are particularly significant, or that might shed some light on binary stellar evolution or theories of capture processes, that are sought, but so far no examples have been found or at least suspected?

By "pairing" I mean a binary object where each is a type of star or a black hole.

Stars can be anything from brown dwarfs to neutron stars. Black holes should be very roughly comparable to stars in size. (I'm not asking about a star in orbit around a supermassive black hole in the center of a galaxy)

For example, recent observations of gravitational wave events have suggested a pair of black holes merging, and a pair of neutron stars merging.
As far as I am aware, there are no known examples of black hole+neutron star (BHNS) binaries (e.g. this paper from 2018 notes that "No BHNS binaries (BHNSs) have been discovered so far by radio surveys"). BHNS mergers should be observable with gravitational wave astronomy, so this situation may not last for too much longer. There is a report of a possible BHNS merger detected by LIGO and Virgo (event S190426c). This event has yet to be confirmed, follow-up searches by Hosseinzadeh et al. (2019) and Goldstein et al. (2019) for transients have failed to find a counterpart to the event.

Binaries containing an sdB star and a neutron star have also not been found, though theoretical models predict they should exist in our galaxy (Wu et al., 2019). Sufficiently close sdB+NS binaries should be strong gravitational wave sources, so LISA may discover them.

Depending on how you want to define various "types" of star, you can probably come up with more examples. For example, there is the concept of singleton stars which have never been members of binary systems or had close encounters with other stars, which by definition have not been found in binary pairings.

There are also some weird categories of objects with few known members. For example there are the LP&nbsp;40-365 stars, which are runaway stars with atmospheres dominated by oxygen and neon, likely the partially-burnt remnants of peculiar type Iax supernovae. None of the four known examples of this class are binary systems, plus the circumstances that lead to their creation makes it seem fairly unlikely that we'll find one in a binary.