Something that's invulnerable is impossible to damage or injure, like the strongest, most rock solid concrete fort reinforced with steel bars. Or Mother Theresa's reputation.
From the Latin invulnerabilis, meaning “not wounding,” came the English invulnerable, an adjective meaning invincible or immune to attack. Some people look to vaccines to make them invulnerable. Others use body armor. Philosopher Henry David Thoreau, on the other hand, relied upon music: “When I hear music, I fear no danger. I am invulnerable."