If Gwafa Hazid leaves the battlefield, any bribery counters will remain where they are. However, without a Gwafa Hazid on the battlefield, creatures with bribery counters on them can attack and block as normal. If another Gwafa Hazid enters the battlefield, its ability will affect all creatures with bribery counters on them, including the ones that received counters from a different Gwafa Hazid.
Creatures with bribery counters on them can't be declared as attackers or blockers. However, if a bribery counter is put on a creature that's already been declared as an attacker or blocker, that creature will continue to attack or block that combat.