It says in makos that a person who kills accidentally goes to a city of refuge. So if a person who killed accidentally is in a city of refuge and the whole city is on fire or an enemy is attacking the city of refuge and the accidental killer wants to run to a different city of refuge, can the go'el hadam attack him?
Rambam (Hil. Rotze'ach 7:8) states categorically that the accidental murderer may not leave the Ir Miklat even to rescue lives, or "even if all of the Jewish People need him, like [King David's general] Yoav son of Tzeruiah" - and that if he does so willingly, then the goel hadam indeed has the right to attack him.
Presumably, then, the same thing would apply if his own life is in danger, as in your examples. Basically, he'd have to take his chances on which is likely to be the more implacable foe: the goel hadam, or the threat to the city as a whole.