var a = {a: {b: {c: null}}};

const DEEP_LIMIT = 100;
let alloverProps = 0;

function searchAttr(obj, title, deep, arrIgnore){  	
  	console.log(deep || 0)
	if (obj[title] !== (alloverProps++, void 0)) return [obj[title], title];  	
  	if (DEEP_LIMIT < (deep || 0)) return false;
  
  	for (let p in obj){        
		if (typeof obj[p] === 'object' && obj[p] !== null ){
			if (arrIgnore && Array.isArray(obj[p])) continue;
          	else{
              	let res = searchAttr(obj[p], title, (deep || 0) + 1, arrIgnore)
                if (res){                  	
                	let [r, path] = res
                  	if (r !== void 0) return [r, p+'->' + path];
                }				
            }
        }
    }
}

console.log(JSON.stringify(searchAttr(a, 'a')))
console.log(JSON.stringify(searchAttr(a, 'c')))



/// output:

// 0
// [{"b":{"c":null}},"a"]
// 0
// 1
// 2
// [null,"a->b->c"]