1.
If you chase someone down , you run after them or follow them quickly and catch them. ( mainly AM )
Ness chased the thief down and held him until police arrived...
For thousands of years chasing down game was the main activity in which humans were involved.
PHRASAL VERB : V n P , V P n (not pron)
2.
If you chase someone or something down , you manage to find them after searching for them.
That’s when I chased her down to be the singer in my band...
Bank officials argued that it is not their job to chase down every asset of every bank debtor.
= track down
PHRASAL VERB : V n P , V P n (not pron)