zadesiti

1. (of misfortune) to befall; to strike
   Porodicu je zadesila velika nesreća. — A great misfortune befell the family.
   Ne znamo šta nas može zadesiti sutra. — We don't know what might befall us tomorrow.
2. (zadesiti se) to happen to be; to find oneself
   Slučajno sam se zadesio u blizini kad se to desilo. — I happened to be nearby when it happened.

In the sense 'befall' it takes the accusative of the person and is usually in the 3rd person.