"Going solo" might mean you actually want to play solo. Because of that, going solo should put you in your own, LOCKED party (or there should be an option to make that the default). You can retain the option to unlock it later, but it should default to locked.

I went solo just a moment ago after joining a PUG with a player who was AFK (or perhaps dual-clienting), so I decided I would rather play alone. About 1/3 of the way through my new solo level, not one but three people popped in. I had JUST gone solo and actually wanted to be solo. I know I could have gone solo and then locked the party, but in the middle of play that much clicking isn't an option. You spawn in the new scene and you have to start killing enemies immediately or they kill you.