What happens if a target becomes ineligible after a card has been cast?
Strangling Soot has an illegal target (only one) as it resolves and therefore fizzles (is countered by game rules due to all targets being invalid). 

When you cast a spell with targets, you check the validity of all targets as it is cast. If any targets are invalid, the spell is "undone" and goes back to where it started. As the spell resolves, it again checks if the targets are valid. If any are valid, it resolves as much as it can; if not, it fizzles. 


  608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. .......