javax.persistence.NoResultException: No entity found for query

Yes. You need to use the try/catch block, but no need to catch the Exception. As per the API it will throw NoResultException if there is no result, and its up to you how you want to handle it.

DrawUnusedBalance drawUnusedBalance = null;
try{
drawUnusedBalance = (DrawUnusedBalance)query.getSingleResult()
catch (NoResultException nre){
//Ignore this because as per your logic this is ok!
}

if(drawUnusedBalance == null){
 //Do your logic..
}

When using java 8, you may take advantage of stream API and simplify code to

return (YourEntityClass) entityManager.createQuery()
....
.getResultList()
.stream().findFirst();

That will give you java.util.Optional

If you prefer null instead, all you need is

 ...
.getResultList()
.stream().findFirst().orElse(null);