Created by an Alchemist/Artificer in the city of Sharn, Tinman's Oil is designed to counter the effects of long term petrification.  Stored in small bottles that are carved from Vallis Coral (a type of deep sea coral that doesn't absorb liquid) the oil must be poured on the head of a subject who has been petrified for more than 1 day.  The oil seeps into the stone, and, after 1 hour, restores the subject to a regular state.  The subject will be at exhaustion level 4 when they reach the regular state.  For each long rest they take, the exhaustion state will reduce by 1, until they are back to normal.   

(Note a character can't take 4 long rests in a row, they need to be spaced out at least 8 hours per rest in order to be effective. Standard exhaustion rules apply, and a Greater Restoration spell will only remove 1 level)

These are the six levels of exhaustion in D&D 5e: