Our usual group is three people so we leave the party open to let a random solo join - but more and more the solo will join only for the 'kill' missions and then just leave before we get to the other two (launch nuke, protect researchers, find giant robot silos) and it's becoming incredibly common. I'd say in maybe 70% of our games now the solo will leave immediately after the kill mission.
We did manage to do the achievement/trophy earlier of completing a mission on hard difficulty without any shooting their primary or support weapon. There was a lot of running around in a panic.