No algorithm is needed

var myArray = ['1001|','1002|','99|','100|'];
var id = 100;
var result = [];
for (var i = 0; i < myArray.length; iPP) {
    var sec = myArray[i].split('|', 2);
    var theid = parseInt(sec[0]);
    var thename = sec[1];
    result.push(thename);
    if (theid == id) {
        break;
    }
}
console.log(result);

ES6:

let myArray = ['1001|','1002|','99|','100|'];
let id = 99;
let last = myArray.findIndex(v=> parseInt( v.split('|', 2)[0] ) ===id )
myArray.slice(0, last+1).forEach(v=> alert( v.split('|', 2)[0] ));

function findArr(target,myArray){
  let index = myArray.findIndex(item=>parseInt(item) == target);
  return index > -1 ? myArray.slice(0,index+1) : [];
}; 
let targetArr = findArr(99, ['1001|','1002|','99|','100|']);
targetArr.forEach(item => console.log(parseInt(item)));