Every player who personally deals at least 10% of the boss's maximum hitpoints gets their own roll of its drop table — not a share of one drop. Two players over the line means two independent rolls, each with its own collection log entries. That same 10% is what earns you the kill count and your slayer task progress, and what makes the kill count toward your daily tasks. One line, everything behind it: clear it and the kill is yours in every sense, miss it and it counts for nothing. Being defeated after you have already cleared it costs you none of it.
Damage from any source counts, including specials and summons, and it resets each time the boss respawns. The bar under the boss's name tracks your own progress toward the threshold: it fills as you deal the 10% you need and turns green when your drop is secured. With the group capped at 8, the top contributor always clears the line, so a kill never comes out empty for everyone. Being defeated does not cancel a drop you had already earned.
Slayer task credit works differently — it goes to everyone still alive at the kill who has that boss as their task, whatever their damage.
While you are in a group fight the server owns your save, so saving, skipping time, buying and Trading Post activity are all locked until you leave with the back arrow.