1.
If a responsibility, duty, or opportunity falls to someone, it becomes their responsibility, duty, or opportunity.
He’s been very unlucky that no chances have fallen to him...
It fell to me to get rid of them.
PHRASAL VERB : V P n , it V P n to-inf
2.
If someone falls to doing something, they start doing it. ( WRITTEN )
When she had departed, they fell to fighting among themselves.
PHRASAL VERB : V P -ing