Cleanups, killing, and death triggers

Damage does not kill. A unit with lethal damage marked stays on the board until the next cleanup, and a cleanup is a fixed checklist that runs between chain items. Deathknell and kill credit both hang off that moment.

Worked example. Your opponent plays Falling Comet, "Deal 6 to a unit at a battlefield", on your Ferrous Forerunner, a 6 Might unit with Deathknell: play two 3 Might Mech tokens to your base. Six damage is marked, but the Forerunner is still on the board while the spell finishes resolving, because a cleanup cannot occur while a chain item is resolving (rule 321). When the spell is gone from the chain a cleanup becomes an Outstanding Task (rule 319.5), and no player receives Priority or Focus in the middle of it (rule 320 and rule 320.1). The cleanup kills the Forerunner (rule 323.4), and the kill is credited to Falling Comet, the spell that resolved just before and dealt the damage (rule 429.5.c). Just before the Forerunner reaches the trash, its Deathknell goes on the chain as a Pending Item, with the unit's location and details noted (rule 808.1.d.2 and rule 808.1.d.3). The Mechs arrive when that trigger resolves. If the Forerunner was your only unit at a battlefield you controlled, the Deathknell now waiting on the chain keeps the turn in a Closed State, so control is not lost in this cleanup, because rule 323.5 needs an Open State (rule 331.1). It is lost in the cleanup that follows once the trigger has resolved, if no unit of yours is there.

The checklist. A cleanup becomes an Outstanding Task at set times, such as after a chain item leaves the chain, after objects enter or leave the board, and after a move (rule 319). If something in a cleanup qualifies for another cleanup, another follows at once, until one changes nothing (rule 322). The tasks run in this order (rule 323). First, a player with at least the Victory Score and more points than every opponent wins (rule 323.1). Second, Attacker and Defender designations are assigned or removed (rule 323.2). Third, every unit with lethal damage is killed and put in its owner's trash (rule 323.4). Fourth, players lose control of battlefields their units no longer occupy, if the turn is in an Open State with no showdown or combat there (rule 323.5). Fifth, unattached gear and runes at battlefields and permanents in the wrong base are recalled, and Hidden cards at battlefields their controller does not control go to the trash (rule 323.6 and rule 323.6.a). Last, showdowns and combats are staged, Contested is removed where it no longer applies, and a staged showdown or combat begins (rule 323.7 through rule 323.13).

Deathknell. Deathknell is short for "When I die, [Effect]" (rule 808.1.c), and it is not a cleanup step. A trigger on its own source leaving the board is processed immediately before the object changes zones (rule 383.2.c.3). The same holds when a Kill instruction does the killing: the unit's death trigger is added to the chain first (rule 429.1.a.1.b). It is added only after replacement effects: if the death is replaced, for example by a recall, nothing triggers (rule 383.2.c.3.a and rule 808.1.d.1). Each instance of Deathknell triggers separately, and the controller orders them (rule 808.2 and rule 808.2.a). Other triggers are different: an object that leaves the zone its trigger is active in at the same moment the condition is met cannot evaluate it (rule 383.2.c.2).

Kill credit and Temporary. A kill in a cleanup is credited to the spell or ability that resolved just before and dealt the damage (rule 429.5.c). In the Combat Cleanup, which inserts "Heal all Units" and "Recall Attackers if Defenders are still present" after the kill step, the sources of the combat damage get the kill (rule 468.1.a.1, rule 468.1.a.2 and rule 429.5.c.2). Temporary is short for "At the start of this permanent's controller's Beginning Phase, before scoring, kill this" (rule 816.1.b). The unit lives until that controller's next Beginning Phase and is killed before scoring, so it cannot hold for a point that turn.

Common mistake. "It has lethal damage, so it is dead and I can't act." It is on the board until the cleanup, but you can't act in between either: no player receives Priority between the end of the spell and the kill.