I am not certain, but I am pretty sure if you have your friends join your fireteam while in the strike it actually splits the strike in two letting your friends join and leaving them with an identical copy but without you. I had this happen while doing ROC strikes. We were down a person and a friend came online. We were chatting in party and I offered to let him join. When he dropped in the other person immediately went away and we carried on from there. Same thing another time when I had two others in the strike with me. Friend dropped into fireteam and the other two dissappeared and we carried on from the point I was at. May be a different explanation for what happened, but maybe something to try?