Sorry I didn't make it out. I saw your posts about the game being on, but something came up at home and by the time I took care of it, it was already almost 9pm.
I think from now on I'm not going to promise anything and just show up if I can. It sucks.
When we ended mid-dungeon in my games, I usually tried to have some sort of in-game explanation for it. For example, the missing PCs got separated from the rest of the party in the dark, cut off by a large group of monsters, etc. The new PCs have been prisoners discovered/liberated in the very first scene of the next session, a separate party lost underground, and a relief force, IIRC.
I also used to impose small penalties on the new PCs. Liberated prisoners didn't have any armor and weapons on them (they were stashed elsewhere by the captors). The lost party didn't have any light sources, rations or water. The rescue party was under attack, etc.
One thing I have also done is say that time passes in between sessions, so the party has actually been holed up underground for several days or a week, laying low. Which gives other PCs time to find them, etc. That convention started back in the days when the game calendar and the real calendar were the same, so if there was a week between sessions, there was a week in game time. I liked that, but I was the only one. Lots of room for hand-waving and off-camera events.